ESI NEWS · 2019. 8. 5. · ESI NEWS Volume 2, Issue 1, Spring 2007 Contents ... European...

The Erwin Schrodinger InternationalInstitute for Mathematical Physics

Boltzmanngasse 9/2A-1090 Vienna, Austria

ESI NEWS Volume 2, Issue 1, Spring 2007

ContentsWalter Thirring and the Erwin Schrodinger

Institute 1

Following Walter by Jakob Yngvason 1

Walter Thirring – A Short BiographicalSketch by Wolfgang L. Reiter 2

Walter Thirring’s Arrival in Vienna by Her-bert Pietschmann 5

Walter Thirring and Austria’s accession toCERN by Wolfgang Kummer 6

Walter Thirring’s Path into MathematicalPhysics by Heide Narnhofer 6

Unmathematical and Mathematical Physicsby Bernhard Baumgartner 8

Gravitational Matters by Helmuth Urbantke 9

Guidelines for Students of TheoreticalPhysics by Walter Thirring 10

Walter Thirring: Probing for Stability byHarald A. Posch 11

Almost 50 Years of the Thirring Model byHarald Grosse 12

A Crossword Puzzle Without Clues by PeterC. Aichelburg 13

Doing Physics with Walter by Elliott Lieb 14

My Contacts with Walter Thirring by AngasHurst 15

Birthday Greetings to Walter Thirring byErnest M. Henley 16

ESI News 16

Current and Future Activities of the ESI 17

Thirringfest 18

Walter Thirring and theErwin SchrodingerInstituteIn August of 1990 Alexander Vinogradovsent a letter to Peter Michor in Vienna withthe suggestion to set up a research insti-tute devoted to mathematics and physicsin Vienna. Setting up such an institutionwas seen as a potentially valuable contri-bution at this time of crisis for the EasternEuropean scientific community: based onthe cultural and scientific tradition in Vi-enna, especially in the field of mathemat-ical physics, a new institute based in Vi-enna could provide a focal point for bothEastern and Western science and an inter-national platform for research in the fieldof mathematical physics.

This initiative was warmly welcomedby Walter Thirring. In a letter to the Minis-ter of Science and Research, Erhard Busek,dated October 18, 1990, Thirring proposedto establish the ‘Erwin Schrodinger Insti-tute for Mathematical Physics’ in Vienna.Thirring’s proposal immediately won thesupport of eminent scientists all over theworld, and Busek responded favourably inDecember 1990.

The society (‘Verein’) ‘InternationalesErwin Schrodinger Institut fur Mathema-tische Physik’ was officially founded inApril 1992, and on May 27 the consti-tutional general assembly of this society

elected Thirring as its president and tookthe formal decision to set up a research in-stitute under the legal framework of the so-ciety.

The Erwin Schrodinger InternationalInstitute for Mathematical Physics (ESI)started its operation in January 1993 underthe presidency and scientific directorship ofWalter Thirring with Peter Michor as ex-ecutive director, and was opened officiallyon April 20, 1993, under the auspices ofVice Chancellor and Minister for Scienceand Research, Erhard Busek.

In 1998 Walter Thirring retired as Pres-ident of the ESI and became its HonoraryPresident. This did not in any way dimin-ish his immensely valuable contributions:even now, at the age of 80, Walter Thirringcontinues to suggest new initiatives and di-rections for the Institute and its scientificprogramme.

This special issue ofESI NEWS devoted toWalter Thirring on theoccasion of his 80thbirthday is a small to-ken of our gratitudefor almost 17 years ofwork, support and ad-

vice for the Institute, and for many years ofpersonal friendship and scientific stimula-tion.

Klaus Schmidt, Joachim Schwermer andJakob Yngvason

Following WalterJakob Yngvason

My first encounter withWalter was in 1976. Thiswas not a personal meet-ing though, I was simplyin the auditorium of theWinter School in Schlad-ming where he lecturedon Stability of Matter.Little did I know then that 20 years laterI would be in Vienna as his successor.

Of course, it is not possible to succeedWalter except in the trivial sense of a tem-poral order in a list of professors of theo-

retical physics at the University of Vienna.Walter’s style, both in his profession andhis life in general is so unique that it wouldbe preposterous even to try to imitate it. Buthis papers, books and lectures continue tobe a standard of reference for the assess-ment of any work in mathematical physicsand have been a constant stimulus for myown work.

Coming back to the Schladming lec-tures of 1976 I recall how I liked the wayWalter presented the case for Stability ofMatter. He did not jump right into the math-ematics but explained first the importanceof the question and then started off with the‘private room’ argument for the electronsand did the ‘back of an envelope’ estimate

of the kinetic and Coulomb energies, com-paring the result also with the analogouscalculations for Bosons and also for gravi-tating particles to bring out the differences.He then commented on the justly famouswork of Dyson and Lenard from the year1967 where stability of matter was provedfor the first time but with an absurdly largeconstant of the order 1014 in the lowerbound to the energy. As Walter remarked,the large constant was solely due to the tourde force method of proof that consisted ofa long sequence of estimates, about 45 inall, loosing a factor of 2 on average eachtime. If you do this 45 times, Walter ex-plained, then you are close to 1014. Afterthese explanations he proceeded with his

2 Volume 2, Issue 1, Spring 2007 ESI NEWS

and Elliott Lieb’s new and beautiful proofbased on Thomas-Fermi theory that goesright to the heart of the matter and producesa reasonable constant. This work is a truemasterpiece of 20th century mathematicalphysics and its extensions and refinementscontinue to be active research topics.

Walter’s textbooks on MathematicalPhysics are marvellous works and thedenseness of information and insights theyprovide is truly remarkable. One reason forthis is Walter’s awesome skill in distill-ing a complicated mathematical argumentinto a few lines. Sometimes the result hasthe character of ‘spiritus concentratus’ thatmust be diluted again to bring it back todrinking strength; this is in fact what I havedone on several occasion when lecturing tostudents. Such elaborations have pedagog-ical merits but I sometimes wonder if I amnot depriving the students of the experienceof being exposed directly to the hard stuff.Also, Walter’s method takes less time and Ihave never in my courses managed to covera comparable amount of material as Wal-ter has apparently done in his courses. But

this is one of the differences in style I men-tioned before.

There is one aspect of Walter’s work-ing style that I sometimes wish I could im-itate: his extreme discipline and organiza-tion. I understand that when he had admin-istrative duties at the University he man-aged them very effectively and kept them intime slots well separated from other things.In this way he had plenty of time for thethings he likes most: doing physics, play-ing the organ and composing music.

Characteristic for Walter’s scientificwork is the breath of topics he has been in-terested in and worked on. In this respecthe is for me the model case of a mathe-matical physicist. One often distinguishesbetween ‘method oriented’ and ‘problemoriented’ approaches in science and some-times mathematical physics is regarded asbeing as a discipline solely defined by itsmethods. I regard this is a misunderstand-ing. In any field there are practitionersthat have acquired some skills in a spe-cific method and spend most of their pro-fessional life in searching for and working

on problems to which these methods canbe applied. In disciplines that rely heavilyon expensive experimental equipment thisstrategy may even be perfectly justified fora limited amount of time. But in physics thetrue aim of the game is to understand hownature ticks at its fundamental level and forthis task the methods have to be chosen tofit the questions attacked.

Walter has worked in Quantum FieldTheory, Elementary Particle Physics, Sta-tistical Physics and General Relativity andmade seminal contributions to all thesefields. He is one of the pioneers of mod-ern mathematical physics, to which I wouldalso count people like Rudolf Haag, ArthurWightman, Hans Borchers, Ludwig Fad-deev, Elliott Lieb, Joel Lebowitz and DavidRuelle, among others, who in the 1960’srealized that there are deep questions inphysics that require deep mathematics fortheir proper understanding and were pre-pared to learn what it takes whenever nec-essary. Carrying on with this tradition is thelegacy for Walter’s followers.

Walter Thirring – A ShortBiographical SketchWolfgang L. Reiter

‘I never wanted towrite an autobiogra-phy. How despicablethose nostalgic warstories of old men ap-peared to me prov-ing what hell-raisersthey had been in theiryouth’.1 With these words Walter Thirringopens a biographical sketch of his earlydays overshadowed by the invasion of Nazibarbarism. He was born on April 29th,1927, in Vienna into a Protestant fam-ily originating from Thuringia (the familyname Thuringer finally became Thirring).His ancestors came to Austria in 1623 asreligious refugees during the times of theThirty Years’ War and later settled in thesmall Hungarian town of Sopron. Hun-gary was then and later a safe haven forProtestants, since the Transleithanian partof the Habsburg empire did not submitto the cuius regio eius religio rule andthe Counter Reformation. His grandfa-ther Ludwig Julius Thirring (1858-1941)moved to Vienna in 1878 to study mathe-matics and physics.

While being of Protestant denomina-tion Walter attended the progressive, non-

elitist and socially oriented Catholic ‘Neu-landschule’. The adolescent boy was soonconfronted with a radical change of society‘which can be arbitrarily deformed in thehands of a demagogue’.2 A few days afterthe occupation of Austria by Nazi Germanyin March 1938 his father Hans Thirring(1888-1976) was dismissed from his aca-demic post. The Gestapo was since then afrequent visitor of the Thirring’s flat.

‘My brother three years older in agehad always been considered a great geniuswhile I was just the small appendage’.3 Ina letter to Walter written from the Russianfront his brother Harald (1924-1945?) ex-pressed no hope of surviving the war. Hecharged his younger brother to keep the sci-entific tradition of the family.4 Without be-ing able to attend school classes, becausein the meantime he had already been con-scripted as a ‘Flakhelfer’ (there he exer-cised his mathematical abilities by misdi-recting the guns until noticing that this wasto no avail) he was provided by his fa-ther with the then standard textbook fortheoretical physics, the ‘Joos’, a superbchoice as Thirring remarks.5 The 17 yearold boy started off to follow the family’sorders issued by his brother. Followinghis grandfather Ludwig Julius who stud-ied with Charles Hermite (1822-1901) inParis and his father Hans, student of Boltz-mann’s pupil Fritz Hasenohrl (1874-1916)and since 1927 full professor of theoreticalphysics at the University of Vienna, it was

now Walter’s turn to close the gap in thefamily’s chain of physicists. Harald did notreturn from the Russian battle field.

Walter had had in mind a quite differ-ent professional career: he wanted to dedi-cate his life to music, playing the piano andcomposing. But the brother’s letter fromthe eastern front overruled Walter’s love formusic. Responsibility for the family and itstradition, ‘Verantwortungsethik’ accordingto Max Weber’s analysis, was the drivingforce — or was it the father’s order uncon-sciously executed by the brother (here weare in genuine Freudian waters) setting thestage for Walter becoming a physicist?

During the last days of World War IIthe Thirrings left Vienna for their sec-ond home at Kitzbuhel not far from Inns-bruck, where Walter began his studieswith the theoretical physicist Arthur March(1891-1957) lacking a proper final exam(Matura). In 1949 he got his PhD fromthe University of Vienna with distinction.The topic of his thesis was the Diracequation (‘Zur kraftefreien Bewegung nachder Dirac-Gleichung’). Paul Urban (1905-1995), assistant at the Institute for The-oretical Physics at the University of Vi-enna, raised Thirrings interests in mesontheory, at that time the talk of the townamong physicists, by engaging him in bor-ing perturbation theory calculations of var-ious cross sections. When he asked if therewere any experimental data available tocheck and verify his calculations he had to

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ESI NEWS Volume 2, Issue 1, Spring 2007 3

be disappointed by his tutor.After having received his PhD Thirring

was granted a scholarship at the Dublin In-stitute of Advanced Studies, where he metErwin Schrodinger (1887-1961), a closefriend of his father from the times of theirstudies with Fritz Hasenohrl. The follow-ing year he spent as a Fellow at Glas-gow University and during the academicyear 1950/51 he held an assistantship at theMax-Planck-Institut in Gottingen, wherehe worked with Werner Heisenberg (1901-1976). Until his first position as a profes-sor of theoretical physics at the Univer-sity of Bern he was ‘on the road’: 1951/52as UNESCO Fellow at the ETH Zurich,where he met the caustic Austrian Wolf-gang Pauli (1900-1958), 1952/53 assis-tant at the University of Bern. In 1953/54he worked at the Institute for AdvancedStudy in Princeton and met Albert Ein-stein (1879-1955). In 1952 Thirring mar-ried Helga Georgiades. The couple has twosons, Klaus and Peter, and four grandchil-dren have since enlarged the family.

In 1954 he returned to Europe as a lec-turer at the University of Bern. The fol-lowing years 1956/57 he was Visiting Pro-fessor at MIT and 1957/58 at the Uni-versity of Washington in Seattle. Duringthis time of academic tramping Thirringwas intensively engaged with problems inquantum field theory, becoming one of itspioneers. Among his co-authors at thattime were Stanley Deser, Marwin L. Gold-berger and Murray Gell-Mann. Several pa-pers on renormalization and dispersion re-lation in particle physics were the result ofthese fruitful co-operations.6 During thisten year period of work at different re-search centres Thirring made a pivotal ex-perience, transnationality of science, an in-sight he brought back to his, at that timeprovincial, native Austria. After one yearas full professor at the University of Bernin 1959 he accepted a call of the Universityof Vienna. Until his retirement in 1995 hewas professor at the Institute of TheoreticalPhysics in Vienna.

From an early stage onward, Thirringwas engaged with the first steps of Aus-tria’s membership of CERN which wasfinalized in 1959, opening doors for ex-perimental and theoretical research on atruly international basis. Since the 1950’sThirring concentrated his research mainlyon theoretical elementary particle physicswith some excursions into other fields ofphysics. When Marietta Blau (1894-1970),who pioneered the photographic methodin particle physics, came back to Austriain 1960 after having left the country as

a Hitler refugee in 1938 and years spentin Mexico and later in the US (ColumbiaUniversity, Brookhaven, Florida), she andThirring formed a group of young stu-dent researchers to analyse bubble chamberphotographs from CERN. This initiativewas a very first bridge between experimen-talists at CERN and physicists in Viennaand thus the starting point of high energyphysics in Austria. Subsequently, the Insti-tute of High Energy Physics of the AustrianAcademy of Sciences was founded in 1966and became the home base for Austria’sactivities at CERN, actively supported byThirring as long term chairman of the boardof the Institute. In 1966 Thirring was madecorresponding and in 1967 full member ofthe Austrian Academy of Sciences.

Thirring’s close ties to high energyphysics found a new stage when he be-came member of the Directorate of CERNas head of the Theoretical Department forthe period 1968 – 1971, a time of impor-tant decisions to be made. The main tasks atthat time were to get the intersecting stor-age ring ISR, based on a concept of theAustrian-born physicist Bruno Touschek(1921-1978), operational and to negotiatethe siting of the next generation accelera-tor, the 300 GeV SPS, which had alreadybeen decided on in 1964 under the direc-torship of another Austrian-born physicist,V. F. Weisskopf (1908-2002). Thanks to theinterventions of the then Director Generalof CERN, Bernard Gregory, the memberstates finally took the wise decision to buildthe SPS at Geneva, against strong lobbyingof several countries to build the machine ona different site somewhere in Europe. Aus-tria took part in this competition and madea site proposal for Gopfritz in the Waldvier-tel, a place surrounded by lovely woods andof perfect geological conditions some hun-dred kilometres north of Vienna!

Interestingly enough Thirring has writ-ten only occasionally on science policyor exposed his opinion on matters be-yond pure science in public. On the oc-casion of the opening of the 10th Schlad-ming Winter School for Nuclear Physicsin 1971 Thirring addressed the audiencewith an analysis of the situation of high en-ergy physics in Europe stressing the impor-tance of fundamental science for the sci-entific development in Europe to counter-act the influence of the leading powers,USA and the Soviet Union. Big sciencehad become the characteristic of researchin fields like particle physics, and Thirringstressed the fact that it is most importantfor small countries to participate in thisgame. Thirring went one step further and

called for new instruments for research inEurope: ‘The real problem of science in Eu-rope seems to me to be how we shall be ableto cope with these challenging fields whichrequire large-scale collaboration. The in-dividual countries are too small to dealeffectively with these branches of scienceand it will be difficult to co-ordinate theintentions and desires of various countriesand various scientific disciplines. Withoutsomething like a European Research Coun-cil [my emphasis] which plans and super-vises science as well as directs the spend-ing of the research money on a Europeanlevel, I can hardly see that we will get any-where’.7 It took quite some time until, in2006, Thirring’s proposal became reality(albeit in a different form) with the foun-dation of the European Research Coun-cil within the framework of the EuropeanCommunity. The incisiveness of his intel-lect had seen a pressing need long before,but the realisation of his proposal needed afurther step of unification and collaborationin Europe transgressing the political modelof CERN.

Thirring started his academic career byand large as a theoretical elementary parti-cle physicist. Interestingly enough by themid 1960’s he shifted his style from tra-ditional theoretical physics to a strongermathematically oriented mode and thisshift goes together with a shift of his re-search interests. As soon as 1967 he pub-lished in Communications in Mathemati-cal Physics.8 His first encounter with El-liott Lieb happened during their stay at theICTP in Trieste in 1968, and subsequentlywhen Thirring invited Lieb to give a talk onjoint work with J.L. Lebowitz on the exis-tence and convexity properties of the ther-modynamical functions of Coulomb sys-tems.9 Thirring found that this result wasso much part of the general physics culturethat even particle physicists ought to knowabout it.10

A period of intense collaboration on theimprovement of the Dyson-Lenard proofof the stability of matter between Thirringand Lieb started in 1974 when Lieb wasSchrodinger Guest Professor at Thirringsinstitute in Vienna. In the following sum-mer Lieb again came to Vienna and thistime they succeeded in directly proving thestability of matter.11 During the followingyears this topic and other problems of theThomas-Fermi-Theory was further investi-gated by both, together with other collabo-rators.

During the years 1976 – 1978 Thirringserved as first president of the Interna-tional Association of Mathematical Physics

http://www.esi.ac.at/ Erwin Schrodinger Institute of Mathematical Physics


(IAMP) and succeeded in developing thisorganisation into an international platform.

Naturally, opinions are split which ofThirring’s achievements should be countedas the most important. He himself leans to-wards the work on the stability of matter. Intrying to do justice to the enormous breathof his oeuvre an assessment is confrontedwith a wide range of subjects. Among hisearly work we find a paper in the field ofapplied statical mechanics, solving a prob-lem in dentistry,12 next in his publicationlist to his important paper on a quantumfield theoretical model of a self-interactingDirac field which bears his name as a toymodel stimulating research to this day.13

Work on gravitational theory is followedby a precursor of the quark model.14 Thenext paper I want to mention here brieflybecause Thirring frequently refers to it notonly in his popular writings: in 1970 thescientific community received with consid-erable scepticism his claim, that under cer-tain circumstances a system, e.g. our sunor a supernova, will exhibit negative spe-cific heat, i.e. the seemingly paradoxicalfact that a system when cooled gets hotterand cooler when heated.15 The later periodof his work is marked by dealing with ques-tions on the ergodicity of quantum systemsand quantum chaos. An excellent overviewof what he has achieved can be found inThirring’s ‘Selecta’ with contributions toMathematical Physics, Statistical Physics,Quantum Field Theory, General Relativity,and Elementary Particle Physics.16

As an author of textbooks his influ-ence extended far beyond the inner circleof students attending his lecture courses.Thirring published advanced introductionsto quantum electrodynamics17 and quan-tum field theory.18 His four volume text-book on mathematical physics, resultingfrom a four term lecture course duringthe 1970’s, is considered as the standardtext in the field, known at that time to hispupils as typed and mimeographed lecturenotes, the green booklets (‘grune Hefte’).19

Thirring’s argument for the selection of thematerial presented in the textbooks is clearand brief, a trade mark of his somewhatterse style: ‘I decided to cover only thosesubjects in which one can work from thebasic laws to derive physically relevant re-sults with full mathematical rigour’.20 Itfollows, Thirring tells us succinctly, thatrelativistic quantum theory and other im-portant branches of physics are not takenup because they ‘have not yet matured fromthe stage of rules for calculations to math-ematically well understood disciplines’.21

This statement, in a sense, sounds very

much like an ex negativo formulation ofThirring’s research programme as a mathe-matical physicist.

Thirring’s autonomy of choice of hisresearch topics is one of the most aston-ishing observations to make regarding hisscientific oeuvre. Till today he is workingon the forefront of mathematical physicsand at the same time he is a very inde-pendent observer of the scene. His view onphysics is void of fashions. Is there — onemay ask — a specific ‘philosophy’ guid-ing Thirring’s physical insight, his intuitionand choice of subject? He never expressedhimself on this delicate point of motivationof his scientific work, as far as I am aware. Iwill try to formulate it my way: the centralepistemological and methodological motorof his style of doing physics is based on adeep intuition concerning the physical rele-vance of a specific problem, combined withthe aim of uncompromising mathematicalrigour.

Communication between scientistsfrom both fields, physics and mathemat-ics, and the use of the most recent math-ematical tools are integral parts of thismode of operation and has manifested it-self on an international scale at the ErwinSchrodinger Institute under Thirring’s ini-tial directorship. The credo of Thirring —and of the ESI — is the following: the ulti-mate criterium for the validity of a physicalargument lies in a rigorous mathematicalproof based on clearly stated premises.This does not mean that a good deal ofphysical inspiration and a strong feelingfor the right way to formulate a physicalproblem are not necessary conditions tofind one’s feet in physics.

This edition of the ESI NEWS wouldnot have appeared and we would not beable to congratulate Walter Thirring onthese pages had he not lent all his sup-port, enthusiasm and last, but not least, hisreputation as a scholar to the initiative byAustrian and Russian physicists and math-ematicians to found an institute dedicatedto mathematical physics in Vienna. With-out Thirring as an outstanding leader andscientist this dream would not have becomereality. Since 1993 his spirit of weaving to-gether the threads of physics and mathe-matics into one texture is manifesting it-self in the Erwin Schrodinger Institute, per-haps Thirring’s most visible achievementas a scientific manager. There is a furtheraspect of the ESI which goes beyond itsscientific work: as a meeting place for re-searchers not only from East and West ofEurope but on the global scale it reflects as-pirations and hopes of Walter’s father Hans

Thirring to promote peace in this world.22

Let me conclude by citing an observa-tion Thirring made on Schrodinger: ‘Forhim [Schrodinger] the so-called exact sci-ences are just a little stone in the greateredifice of a philosophical world view’.23

Considering Thirring’s dedication and lovefor music, playing the organ and compos-ing, together with his religion-based insightinto the great cosmic fabric we may bewell justified to take Thirring’s words onSchrodinger as a sort of testimony of hisown world view.24

Notes1 ‘Ich wollte nie eine Autobiographie schreiben

. . . Wie jammerlich schienen mir doch die nostal-gischen Kriegsgeschichten alter Herren, mit denensie beweisen wollten, was sie in ihrer Jugend furTeufelskerle gewesen waren’. Walter Thirring, Bi-ographical & Bibliographical Series of Classics ofWorld Science. S.S. Moskaliuk, ed., Kyiv 1997, p. 12.

2 ‘. . . in der Hand eines Demagogen . . . beliebig de-formiert werden kann’, Ibid., p. 57.

3 ‘Mein Bruder war drei Jahre alter als ich und galtschon immer als das große Genie, wahrend ich nurdas kleine Anhangsel war’, Ibid., p. 47.

4 ‘die wissenschaftliche Tradition unserer Familieweiterzupflegen’, Ibid., p. 47.

5 ‘. . . eine treffliche Wahl’, Ibid., p. 47. GeorgJoos, Lehrbuch der theoretischen Physik. Leipzig:Akademische Verlagsgesellschaft 1932.

6 Cf. e.g. W. Thirring, M. Gell-Mann and M. Gold-berger, Use of Causality Conditions in Quantum The-ory, Phys. Rev. 95 (1954) 1612-1627.

7 W. Thirring, High Energy Physics and Big Sci-ence, Acta Phys. Austr., Suppl. VIII (1971) 12-20.

8 W. Thirring, A. Wehrl, On the MathematicalStructure of the BCS-Model. Comm. Math. Phys, 4(1967), 181-189.

9 J.L. Lebowitz, E.H. Lieb, Phys. Rev. Lett. 22(1969) 631-634.

10 Walter Thirring, Biographical & BibliographicalSeries of Classics of World Science. S.S. Moskaliuk,ed., Kyiv 1997, p. 221.

11 E.H. Lieb, W. Thirring, Bound for the Kinetic En-ergy of Fermions Which Proves the Stability of Matter.Phys. Rev. Lett. 35 (1975) 687-689. Errata 35 (1975)1116.W. Thirring, Stabilitat der Materie. Naturwis-senschaften 73 (1986) 705.

12 W. Thirring, T. Hromatka, Uber die Statik fed-ernd abgestutzter Freisattel. Deutsche ZahnarztlicheZeitschr. 7 (1952) 209.

13 Walter E. Thirring, A Soluble Relativistic FieldTheory. Annals of Physics 3 (1958) 91-112.

14 W. Thirring, Three-Field Theory of Strong Inter-actions. Nuclear Physics 14 (1959/60) 565-577.

15 Walter Thirring, Systems with Negative SpecificHeat, Z. f. Phys. 235 (1970) 339-352.

16 Walter E. Thirring, Selected Papers of WalterE. Thirring. Providence, Rhode Island: Amer. Math.Soc., 1998.

17 W. Thirring, Einfuhrung in die Quantenelektrody-namik. Wien: Deuticke 1955. Principles of QuantumElectrodynamics. New York: Academic Press 1958,2nd ed. 1962. Russian Edition.

18 Ernest M. Henley und W. Thirring, Elemen-tary Quantum Field Theory. New York: MacGraw-Hill, 1962. [German transl.: Manfred Breitenencker],Elementare Quantenfeldtheorie. Mannheim, Wien,Zurich: Bibliographisches Institut 1975. Russian undJapanese editions.

19 W. Thirring, Lehrbuch der MathematischenPhysik. Wien, New York: Springer Verlag 1977



– 1980. Band 1: Klassische Dynamische Systeme.Band 2: Klassische Feldtheorie. Band 3: Quanten-mechanik von Atomen und Molekulen. Band 4: Quan-tenmechanik großer Systeme.

20 W. Thirring, Lehrbuch der MathematischenPhysik. Wien, New York: Springer Verlag 1977 –1980. Band 1: A Course in Mathematical Physics.Classical Dynamical Systems. New York, Wien:

Springer-Verlag, 1978, p. xi.21 Ibid.22 Brigitte Zimmel, Gabriele Kerber (Hrsg.), Hans

Thirring. Ein Leben fur Physik und Frieden. Wien,Koln, Weimar: Bohlau 1992.

23 ‘Fur ihn waren die sogenannten exakten Natur-wissenschaften nur ein Steinchen in dem großerenGebaude einer philosophischen Weltsicht’. W.

Thirring, Einleitung in Erwin Schrodinger, Gesam-melte Abhandlungen, Band 4, Allgemeine wis-senschaftliche und populare Aufsatze. Wien: Verlagder Osterr. Akad. d. Wiss. 1984, S. xii.

24 Walter Thirring, Kosmische Impressionen. GottesSpuren in den Naturgesetzen. Wien: Molden 2004.

Walter Thirring’s Arrivalin ViennaHerbert Pietschmann

In 1959 a number ofgraduate students atthe Institute of Theo-retical Physics of theUniversity of Viennawas eagerly waitingfor the arrival of Wal-ter Thirring as newhead of the Institute. Erwin Schrodingerhad retired the year before and the onlyother (associate) professor of theoreticalphysics, Theodor Sexl, refused to teachQuantum Mechanics for personal reasons,although he was expert in Nuclear Physics.We graduate students had to organize pri-vate Seminars in order to learn QuantumMechanics and Field Theory from text-books. (For Quantum Mechanics we hadchosen Dirac’s book — not exactly the eas-iest way into this chapter! Field Theory welearned mostly from Walter’s first book onQuantum Electrodynamics.)

When Walter Thirring arrived, manythings changed spontaneously — the Insti-tute was transformed from a historic placeto a modern research establishment. Need-less to say, that he taught all the mod-ern subjects in his course on theoreticalphysics; but at that time it was almostequally important (as well as surprising)that the Institute now had its own secre-tary! With research grants from the UnitedStates, Walter could open an experimen-tal appendix to the Institute of TheoreticalPhysics: a group evaluating bubble cham-ber photographs from CERN which latergrew into the Institute for High EnergyPhysics of the Austrian Academy of Sci-ence. (After returning from CERN, my firstjob with Walter was to support this groupwith theoretical advice.)

Many prominent guests came to Vi-enna to lecture and stimulate our research.Some of them came for a longer period andcreated an international atmosphere whichalso attracted young postdocs. (One ofthem was A.P. Balachandran from Madras,

with whom I published the first papers onCurrent Algebra.)

Due to Walter’s US grants, we werealso able to report our research results atinternational conferences or — for exam-ple — travel to the United States to lectureabout our work. (In this way, I could reportour results on Current Algebra in 1963 atsix American Institutes.)

We younger physicists greatly admiredWalter’s physical intuition and ability todo calculations in the most simple andstraightforward manner. Indeed, when hewrote his textbook with Henley, Ranningerand I had to check the equations. At onepoint, we were unable to get from one lineto the next in spite of prolonged and greateffort. Of course we were quite ashamedwhen we came to Walter to confess. He wasnot the slightest annoyed but simply wentto the blackboard, wrote down an Ansatzfrom general symmetry arguments, did theremaining algebra in his head and said withsatisfaction: ‘Don’t worry, its OK!’. I haveto add that we were relieved when a fewdays later a letter came from Jacobson andHenley asking Walter to add one line forthey also had to work for some time beforethey found the right way to check this equa-tion.

In the early sixtieth there was a fiercefight among particle theorists as to whatwas the future theoretical basis for the de-scription of elementary particles. Doubledispersion relations were the fad of a largegroup of theorists and many believed, thatLagrangian field theory was old-fashionedand had to be overcome. Indeed, some re-spectable Universities cancelled all con-ventional field theory courses and replacedthem by ‘S-matrix theory’. A culminationpoint in this fight was the publication of apaper by Zachariason in which he claimed‘we shall construct a model field theorywhich is ... not defined in terms of a La-grangian’. If this were possible, it wouldbe quite a victory for the believers in ‘S-matrix theory’.

Walter’s intuition told him that this‘was not the true Jacob’ (to use a for-mulation of Einstein). For Walter it wasquite obvious that Lagrangian field theorycould not be abandoned! Soon after the ap-

pearance of Zachariasons paper, he pub-lished a paper called ‘Lagrangian Formula-tion of the Zachariason Model’. Today weall know that he was right, for the StandardModel of Elementary Particles is of coursebased on a huge Lagrangian! But in thosedays it was a minority opinion and not at allobvious. (My own Habilitation was basedon the ‘Zachariason-Thirring-Model’)

In 1966 I worked with Walter on thequark model of elementary particles. Dur-ing these happy days I learned a lot andagain I could admire Walter’s physical intu-ition. For the benefit of younger colleagueslet me just tell one story about the old days:We had to work out a three-particle phasespace integral, but in those days there wereno computers! So we shared the work: Idrew the integral on a then often used graphpaper and counted the squares. Walter hada slide-rule of one meter length and did arough computation. At the end, we usedan electric calculator which was able toperform the four basic algebraic manipu-lations. Walter, working on his slide-rule,said the numbers aloud and I typed theminto the calculator. In this way — after anhour of work — we did the integral numeri-cally. And this was just about 40 years ago!Times have changed rapidly.

Since 1968 I had my own chair in The-oretical Physics, so I was now Walter’s col-league. I am very grateful to Walter for thefact, that we always had a warm and per-sonal climate at the Institute; the usual ri-valries and quarrels among colleagues weretotally absent during all these decades tothe very day! To me, this is one of the finestaspects of Walter’s personality, for I couldnot have lived in an atmosphere of tension,not to mention fight. (Our common interestin music may have been helpful.)

Around this time, Walter became direc-tor of the theory division at CERN for threeyears. It is coincidental, that just then hechanged his field of interest from particlephysics to mathematical physics. One maydeplore the loss of such an intuitive physi-cist for particle physics, on the other hand,one may applaud the gain for mathemati-cal physics of a person with such a greatphysical intuition. Without it, mathematicalphysics may too easily become esoteric.



Walter Thirring andAustria’s Accession toCERNWolfgang Kummer

In the 1950’s thephysics institutes inAustria in general andespecially at the Uni-versity and the Tech-nische Hochschule Vi-enna were still in anextremely poor shape:

laboratories still showed the marks ofbombings, obsolete equipment — if avail-able at all — from pre-war times, amongthe students many former soldiers of theGerman army with large deficits in sec-ondary schooling and a very inhomoge-neous body of teaching personal, becauseonly in rare cases well qualified professorshad somehow survived the nazi regime.Also the motivation for senior Austrianphysicists abroad to return into such anenvironment (moreover at ridiculously lowsalaries) was not pronounced for under-standable reasons. Under these circum-stances it appeared somewhat of a miraclethat it became possible to recruit WalterThirring as a successor to his father Hansfor the professorship of theoretical physics

at the University Vienna. A fortuitous com-bination of supports from quite different(yes, also opposite political) camps createdthe necessary boundary conditions.

How Walter immediately made his in-stitute a focus of international importancein the fields of quantum field theory andmathematical physics will not be describedhere. Instead due credit must be given tohis successful activities regarding Austria’saccession to the European laboratory forHigh Energy Physics CERN. This organi-zation had been created in 1952 as an ex-emplary European effort to collaborate inthe field of fundamental physics at the sub-nuclear level. For Walter is was inconceiv-able to enter the map of top level physicsresearch without being a member in thenew and — as it turned out soon — ex-tremely successful enterprise.

Especially in small countries like Aus-tria the decision to join CERN to this dayusually faces considerable resistance fromdifferent opponents: finance ministers hes-itate to pay large membership fees to in-ternational organizations, most of whomdo not exhibit a glamarous reputation foreffectiveness. Even more importantly, thedear collegues from other fields of physicsand science in general deplore the amountof money which, in their opinion, couldbe invested much more fruitful in their

own fields. Powerful arguments in favour,however, usually come from the politicalside (‘European solidarity’), but especiallyfrom the lobbying by industry which al-ways found CERN and its top require-ments for technological products an impor-tant competitive meeting place. Clearly thelast point did not apply to Austria at thattime. As a young nobody I, of course, neverknew any details about the mechanisms ofthe political interventions of Walter andhis congenial partner Fritz Regler, an ex-perimental physicist from the TechnischeHochschule, who politically covered the‘right’ wing. After some ups and downs thefortunate consequence was the formal ac-cession of Austria to CERN in 1959. How-ever, for Walter Thirring is was evident thatthis membership without proper activity inAustria was useless. Therefore, with thehelp of financial support from a US founda-tion he created the ‘Plattengruppe’, an ini-tially small group of doctoral students, whoevaluated the tracks of elementary particlesin photographic plates which had been ex-posed to the new high energy acceleratorat CERN. This group represented the coreof the Institute for High Energy Physics atthe Austrian Academy of Sciences whichstarted its work officially in 1966 — againthanks to the joint efforts of Thirring andRegler. The rest ist history . . .

Walter Thirring’s Path intoMathematical PhysicsHeide Narnhofer

When looking at Wal-ter Thirring’s publi-cation list in orderto determine a pointof transition fromelementary particlephysics to mathemat-ical physics one soonrealizes that there was no turning point:there was a continuous evolution in thesense that he always wanted to make rig-orous statements. Only the mathematicaltools he used got sharpened in the pro-cess. This process reflected a general ten-dency in the second half of the last century:physicists realized that understanding someparts of physics could benefit enormouslyfrom applying more advanced mathemati-cal tools.

I remember that Walter told me a joke:‘In the first part of the last century it wassaid that the only mathematical tools nec-essary for physics were a good knowl-

edge of the Greek alphabet.’ But alreadyin 1950 Walter was giving a seminar onthe scattering matrix in elementary parti-cle physics and Bruno Touschek, a physi-cist with strong interests in experimentalphysics and less in the mathematical beautyof the theory, raised the question whetherWalter could control the error in the pertur-bative calculation of the scattering matrix.As a consequence Walter tried to controlthis error and had to observe the divergenceof perturbation theory in quantum field the-ory (1952).

Walter also in daily life wants thingsto be clear and straight and is disgustedby any escapes into ambiguity. Thereforeit was clear that he was not willing to ig-nore this fact of divergence and so he waslooking for statements where he was notforced to trust arguments without a pro-found basis. In quantum electrodynamicsrenormalization seems to offer such a ba-sis. The Thirring model (1958) allowed anexplicit solution without referring to anyperturbation expansion. The search for thegroup structure in the family of observa-tions in particle physics (1958) could alsobe formulated in a profound mathematical

language. But already here Walter realizedthat it is worthwhile to deepen the mathe-matical background.

An important ingredient of this deep-ening of his mathematical understandingwas the good contact with the mathemati-cal department. With Leopold Schmettererhe started to have joint seminars withthe purpose not so much to teach stu-dents but out of the desire that he himselfwanted to learn the mathematical concepts.Schmetterer and Thirring studied Pontrya-gin’s book on continuous groups. I remem-ber a seminar on ergodic theory based ona course by Konrad Jacobs. In additionWalter followed an advanced course onthe theory of manifolds given by EdmundHlawka. I remember him sitting among thestudents two rows in front of me. He wouldhave enjoyed a joint research project withHlawka, clarifying how general relativity isbased on the covariance of general mani-folds while maintaining the evidence of aRiemannian metric. But for some reason orother this cooperation did not work out.

In the meantime Walter covered all oftheoretical physics in a course lasting sevensemesters. This required going into de-



tails in various disciplines, and as a con-sequence he got attracted to various sub-jects of theoretical physics that were closeto his taste of combining rigour with intu-ition. But he was also attracted by the factthat some problems were asking for moredelicate mathematics.

We can compare Walter’s approachto more mathematically minded problemswith the evolution of mathematical physicsas a new discipline. In 1960 the Jour-nal of Mathematical Physics was founded,where the term ‘Mathematical Physics’indicated a shift of emphasis towards amore mathematical outlook on ‘Theoreti-cal Physics’. In 1965 the Communicationin Mathematical Physics with the chief ed-itor Rudolf Haag followed. Both journalsstarted with articles on quantum field the-ory and statistical mechanics. In the firstvolume of CMP you can find the descrip-tion what we should understand as mathe-matical physics, unfortunately this part dis-appeared in later volumes:

It is one of the goals of this jour-nal to generate among mathematicians anincreased awareness and appreciation ofcurrent problems in physics, just as we arehoping to acquaint a growing number ofphysicists with methods and results of mod-ern mathematics. This should not be inter-preted as an encouragement of physicists toconfine themselves to rigorous mathemat-ical argumentation. Conjectures, intuitivejudgement and plausibility arguments in-deed have their place, so long as it is madeclear that they are not regarded as proofs.

Evidently Walter was attracted by thisspirit. In 1967 he published for the firsttime in CMP, together with Alfred Wehrl,a paper on the BCS-model where they hadto combine ideas of convergence with ana-lytic considerations.

But as proposed in CMP, he also en-joyed picking up new methods. I remem-ber my thesis on various conductivity prob-lems. The task was to control in differentsettings the time evolution and this waspossible by calculating the integral kerneland extracting from this kernel the desiredinformation. However, in a joint publica-tion Walter added an appendix that was notreally necessary but offered the chance tostudy in an explicit example the differencebetween self-adjoint and hermitian opera-tors, a fact that nowadays is standard formore mathematically minded physicists,but in those days had just become apparent.

In 1968 Walter moved to CERN inGeneva, the European center to do elemen-tary particle physics. But Walter, though al-ways very interested in this field, concen-

trated on other things. He started to studythe book of J. Dieudonne on FunctionalAnalysis. He was so much attracted by thisfirst volume that he offered to Dieudonne toread the corrections of the following vol-umes with the motivation that this wouldforce him to study all the theorems care-fully and in detail.

But there followed another experiencewhere the power of mathematics was im-portant. Whereas in disproving the conver-gence of perturbation theory in quantumfield theory he had to realize how mathe-matics can falsify intuition, now he expe-rienced how mathematics justifies good in-tuition even if this intuition is against com-mon knowledge. He had to argue heavilywith the referee that his result on negativespecific heat was correct, but even more,this struggle convinced him that this resultwas not only correct but also relevant: re-search on the effect of gravitation in starsfollowed. Finally he was happy that the dy-namical part of the theory could also be jus-tified by computer simulations.

In the meantime important progress inmathematical rigour in quantum field the-ory was made as well. Back in Vienna hepicked up this project in a seminar. But dif-ferently to previous seminars, these studiesdid not inspire him to do his own research. Ican only imagine what was the reason: thiswas mathematics that was against his atti-tude. Mathematically rigorous perturbationtheory in quantum field is a hard job. It isas if you had to find your way in a junglewith the vague hope that after heavy strug-gles some clearing might appear where youwould find some insight into what is im-portant and what not and, at last, some in-tuition. We now know that this hope wasnot quite in vain and that some new math-ematical structures really turned out to berelevant. But this is not the way how Wal-ter enjoys research. He wants to start withintuition and then to hunt for the appropri-ate rigorous arguments that would justifyhis intuition. The more tricks are necessarythe more fun.

Somehow typical for this attitude is aresult on the continuity of entropy that wasneeded for the definition of dynamical en-tropy. I offered a characterization with thenecessary dependence on the dimension,based on the idea that first you convinceyourself that the largest variation occurs inthe abelian case and then you estimate thisabelian situation. I was too lazy to calcu-late the explicit numbers on which Wal-ter insisted. On the other hand, he consid-ered my arguments too boring. Instead heused some integral equations, some resol-

vent equations, some trace estimates andwith the appropriate mixture of these argu-ments he got explicit numbers. Of coursethese numbers were not optimal. The opti-mal estimate was carried through by MarkFannes on the basis of my idea and hassince found its way into the literature.

As I mentioned earlier, Walter’s re-search happened at the time when more ad-vanced mathematics entered into physics.The necessity to control convergence wasof course always present. Now it becameapparent that one has to be careful inchoosing the right topology. Puzzled byscattering theory, Walter realized that thenorm topology is useful if you concen-trate on the invariance of the group (heretime translation) but one has to revert tothe strong topology to understand the timelimit and to the weak topology to incorpo-rate the existence of bound states. WhenI was a student, in the textbooks youjust found an explanation on the basis ofdifferential equations. In his course Wal-ter taught me how to switch between theviewpoints and apply both ideas of differ-ential equations and of operator algebrasand, here especially, the power of differenttopologies.

Another viewpoint close to Walter’sheart is the inspiration coming from clas-sical mechanics. What can be inherited andwhat becomes different? Here the formula-tion of classical mechanics in phase spaceis tailor-made, and quantum theory entersby adding correction terms and by control-ling them by estimates in weighted Sobolevspaces. It is still a problem that puzzlesWalter and where he has not given up, thatinequalities so far do not give the numeri-cal bound on stability of matter that his in-tuition from classical phase space offered.Here we observe another element in his at-titude to mathematical physics: existenceproofs are of course important, but you canonly be sure to understand the essentialfacts if you can produce numbers that areclose to the numbers observed in experi-ment.

Stability of matter is a result that he ob-tained jointly with Elliott Lieb. This collab-oration was extremely fruitful and inspir-ing. Walter and Elliott argue on the samefooting and are interested in the same kindof problems. In their joint work it is impos-sible to assign the various ideas to one orthe other. This also becomes evident in afictitious dialogue that Walter wrote on theoccasion of Elliott’s sixtieth birthday. It isnot complementarity but harmony that in-spires and is the source of success.

What were the important achievements



of mathematics that inspired physics in thishalf century? There was the role playedby different topologies. Another examplewas the realization that for thermodynam-ics and quantum field theory one needs theinitially unfamiliar type III algebras. I re-member that as usual I was reading thehandwritten manuscript of his book beforeit went to Franzi Wagner to be typed. ThereI found the sentence: ‘Unfortunately in thethermodynamic limit the algebras turn outto be type-III.’ This raised a discussion thatmade Walter remove the word ‘unfortu-nately’, though he did not go as far as towrite ‘fortunately’ as I had suggested: thisis really the source that enables us to findqualitatively different behaviour in the mi-croscopic and macroscopic world withoutthe necessity to draw a sharp border.

The Tomita-Takesaki theory, discov-

ered more or less independently by math-ematicians and physicists, makes it possi-ble to make statements on ergodic proper-ties in the thermodynamic limit also in thequantum setting, quite in the spirit of Boltz-mann. Mathematics developed further inthis direction. Alain Connes inspired theconnection between various disciplines ofmathematics and founded the concept ofnoncommutative manifolds. Together withtopology this opened the possibility to findconnections between the microscopic andmacroscopic world. Walter was always in-terested in these developments; however,they did not really inspire his intuition. Heis not a mathematician who is looking forbeautiful structures, but he uses physicalmodels as inspiration. Walter is a physi-cist with all his heart whose imagination isvery much influenced by what can be ob-

served. The macroscopic world is the worldwith which we are familiar, and from thismacroscopic world he looks for his inspi-ration for the quantum world that he wantsto build on exact mathematical statements.

This note presents of course a ratherpersonal view, resulting from many dis-cussions and anecdotes that Walter toldme, and observations in our collaboration.Yet memory can be deceptive and I apolo-gize for possible errors and misinterpreta-tions. In any case I do want to thank Wal-ter for the profound education and guideto relevant problems, and even more for along collaboration in which I explored thebeauty and the fun in guessing, substantiat-ing the wishful thinking and finally huntingfor the justification. This is one of the waysto attack physical problems and Walter hasalways been a master in it.

Unmathematical andMathematical PhysicsBernhard Baumgartner

My first impression ofWalter Thirring was ata talk on the thermo-dynamics of stars. Hewas at that time direc-tor of the theory divi-sion at CERN, visitinghis home university inVienna. I was a student of physics at thetime. Having fallen in love with mathe-matics at the beginnings of my studies,but being mainly interested in physics, Iwas happy to hear about the existence of‘Mathematical Physics’. And this branchof physics was led in Vienna by WalterThirring, well known in the physics com-munity (and also beyond). Now I saw thisman of high reputation, short and sturdy,talking about such a big object — a star!– without much ado, but with certitude:‘The star gives away energy, contracts, andbecomes hotter.’ For me as a student, thiswas breath-taking — wasn’t this contraryto text-book physics? A ‘Negative SpecificHeat’! But Walter Thirring together withPeter Hertel had proved this with math-ematical rigour,1 followed by investiga-tions including more details.2 So I got ac-quainted with Mathematical Physics, ap-preciating its exactness.

Only in later years I realized that thiswas just one of the extremal points of sci-ence. Another one was actually the begin-ning of any investigation: it is the art ofmodel building, using intuition and ‘Un-mathematical Physics’. Each model of a

system is thought to represent some spe-cific aspects of nature. To be able to con-centrate on those elementary details of nat-ural laws which are essential to what is go-ing on, in order to highlight the principles,one has to discard the other details. In themodel for stars mentioned above one disre-gards relativity, the multitude of elements,and — hard to swallow — the nuclear re-actions. On the other hand one has to in-vent some unnatural hypotheses: contain-ers for the stars and a limit of particle num-bers going to infinity, coupled with a limitof the volume going to zero, keeping theproper relations between mass, size, energyand temperature. This is a kind of Thermo-dynamic Limit adapted to Thomas-FermiTheory.

The fact that such a procedure is sound,not crazy, is realized by making obser-vations in the realm of UnmathematicalPhysics, also designated by Walter Thirringas Großenordnungsphysik (physics of or-ders of magnitude). In the case of a starwith 1057 electrons and positrons in a vol-ume with diameter 1.4 ·109m it tells us thatthe system behaves not really differentlyfrom its description by Thomas Fermi the-ory. Only to reach the goal of indisputablemathematical exactness one has to considerthe particles as confined and has to enactthe limiting procedures.

For the readers coming from otherfields I would like to point out some ofthe ideas: in the model which has to repre-sent the thermodynamic properties of stars,one discusses a gas of Fermions. In realityeach star radiates away energy and mass,no container exists. But in mathematicalinvestigations of statistical mechanics onehas to incorporate a vessel in order to pre-

vent evaporation. Considering the orders ofmagnitude one finds that this evaporation is‘slow’ in comparison with both the move-ments of particles and the approach to lo-cal thermal equilibrium, the error in dis-carding it for the moment is small. Thencomes an important mathematical ingre-dient: the Virial Theorem. It implies thatlowering the total energy leads to contrac-tion, to the rise of kinetic energy and to therise of temperature. These changes appearin mathematical investigations as functionsof the theoretical input, whereas in realitythey happen in the course of the birth ofa star, followed by the ignition of nuclearfusion. Again these changes of the con-stituents happen much more slowly thanthe local processes establishing the thermo-dynamic equilibrium. Of course it wouldnow be interesting to discuss the history ofthe theory of stars: how Lord Kelvin esti-mated that chemical reactions, as for ex-ample the burning of coal, give less energythan gravitational contraction; that this isstill not enough, enabling a shining of thesun for only some millions of years; alsohow Houtermans and Gamow found outthat nuclear fusion was the main source ofenergy. It was also of great importance thatthe mathematically exact discussions of themodel describe an unusual kind of a phasetransition, related to the collapse of a starafter the nuclear fuel has been consumed.

Use of ‘Großenordnungsphysik’ far-sightedly reveals that throughout history allthe ‘giants of science’ (on whose shoul-ders we are standing) had the right intu-ition to create models, followed by rigor-ous investigations only afterwards. How-ever, the final presentation is often the otherway round: first comes the law, then the



unmathematical popular explanation. Forexample Newton’s Third Axiom, ‘To anyaction there is always an equal and op-posite reaction’ is followed by ‘If anyonepresses a stone with a finger, the finger isalso pressed by the stone’.3 For the ‘aver-age’ scientist, however, the danger of mak-ing fundamental errors in following mis-conceptions is not to be ignored. So, upto the middle of the twentieth century, lit-tle Unmathematical Physics can be foundin textbooks. But nowadays the enormousamount of detail in modern physics ne-cessitates its use in order to get a gen-eral picture. Walter Thirring gave a courseon such themes, perhaps relaxing somehowafter having finished the first draft of hisenormous four-volume work on mathemat-ical physics. At the start he stated its motto‘Es wird nie eine Gleichung aus der an-deren folgen (‘Never will one equation fol-low from the other one’).

Here is the list of contents of Thirring’scourse on Unmathematical Physics:

• Gravitation (astronomical data in or-ders of magnitude for earth, moon, sun,Jupiter, milky way and the universe;the virial theorem and its applications;clouds of gas);

• Electromagnetic phenomena in atomsin a semiclassical way a la Bohr-

Sommerfeld theory and its relativisticcorrections;

• Compressibility of atoms and its use infinding the changeover from planets tostars;

• Structures of atoms;• The role of the Pauli principle in atoms

and stars;• Chemical binding;• The Periodic System of the elements;• The question concerning existence of

negative ions (‘H−− zerbricht beim An-schauen’ (‘H−− breaks when lookedat’). and ‘There are three wrong proofsfor its non-existence’);

• Oscillations and rotations of molecules;• Aspects of solid state physics;• Black body radiation, its use to deter-

mine the temperature of the solar surfaceby ‘Daumenpeilung’ (taking a bearing byrule of thumb), and some aspects of alight bulb;

• Spectral lines (semiclassical aspects oftheir formation and line width);

• Entropy (orders of magnitude, Gibbsparadox, photons, phonons, Fermions)

(My thanks go to Helmuth Urbantke for keepingthe records.)

The spirit of this course provided mewith a firm foundation for my lectur-ing on such diverse themes as solid statephysics (together with Gero Vogl), physics

for prospective teachers and Principles ofModern Physics (a lecture course initiatedby Herbert Pietschmann). Walter Thirringis still a good source of ideas in this spirit.4

His influence has been and will always beof immeasurable value.

Notes1 W. Thirring, Systems with Negative Specific Heat,

Z. Phys. 235 (1970), 339–352.P. Hertel, W. Thirring, A soluble Model for a

System with Negative Specific Heat, Ann. Phys. 63(1971), 520–533.

P. Hertel, W. Thirring, Free Energy of GravitatingFermions, Commun. Math Phys. 24 (1971), 22–36.

P. Hertel, W. Thirring, Thermodynamic instabilityof a system of gravitating Fermions, in Drr H.P. (Ed.),Quanten und Felder. Braunschweig: Vieweg, 1971.

2 P. Hertel, H. Narnhofer, W. Thirring, Thermody-namic Functions for Fermions with Gravostatic andElectrostatic Interactions, Commun. Math Phys. 28(1972) 159–176.

B. Baumgartner, Thermodynamic Limit of Corre-lation Functions in a System of Gravitating Fermions,Commun. Math Phys. 48 (1976), 207–213.

B. Baumgartner, H. Narnhofer, W. Thirring,Thomas-Fermi Limit of Bose Jellium, Ann. Phys. 150(1983), 373–391.

3 Isaac Newton, The Principia, A new Translationby I. Bernard Cohen and Anne Whitman. Berkeley,Los Angeles, London: University of California Press,1999.

4 W. Thirring, Kosmische Impressionen. GottesSpuren in den Naturgesetzen, Wien: Molden Verlag,2004.

C. Faustmann, W. Thirring, Einstein entformelt,Wien: Seifert Verlag, 2007.

Gravitational MattersHelmuth Urbantke

In 1959 W. Thirringwas appointed as fullprofessor at the Uni-versity of Vienna andimmediately startedhis 7-semester lecturecourse on TheoreticalPhysics. This lecturecourse was accom-panied by a set of mimeographed notesGuidelines for Students of TheoreticalPhysics which are reproduced on p. 10.

In his Classical Electrodynamicscourse he included, as an appendix, hisalternative special-relativistic approach toGeneral Relativity (GR), based on two ofhis papers.1 This is how many of us wereintroduced to the subject. In particular, Ro-man U. Sexl took up this approach andused it to classify rival theories of GR intheir linear approximations.2

The year 1965 constituted a turningpoint in Thirring’s interests, directing themtowards mathematical physics — perhapsalso triggered by a seminar, organizedjointly with the mathematician Leopold

Schmetterer, on I.E. Segal’s (then) recentbook Mathematical Problems of Relativis-tic Physics.3 On visiting the London con-ference on GR that year, Thirring becameimpressed by the power of the geomet-ric arguments of Roger Penrose in fight-ing his battle with the Landau-Lifshitz-Khalatnikov school concerning singulari-ties in GR. While the buildup of a groupworking on GR in the following years wasleft largely to R.U. Sexl, Thirrings maincontribution to gravitational physics is non-relativistic: his quantum statistical analysisof stellar equilibrium from first principles.4

In the relativistic regime, i.e. in GR, a con-tribution was to point out advantages of theuse of differential forms, in particular in thecontext of the variational formulation, con-servation laws and energy ‘pseudo-tensors’(which were formerly based only on coor-dinate bases). This got published in the sec-ond volume5 of his four-volume textbookon Mathematical Physics.

This textbook, referred to as ‘mon-umental’ by Nobel Laureate S. Chan-drasekhar upon a visit to Vienna, firstappeared in the form of mimeographedlecture notes of a four-semester courseon mathematical physics and was subse-

quently published by Springer Verlag (sev-eral editions, from 1977 on). The basicidea was to include only subjects whereit is now possible to go from fundamentallaws to physically relevant results withoutmathematical gaps, thus eliminating whatW. Pauli called ‘wishful mathematics’ andW. Thirring calls ‘Darwinian physics’. Incompensation, each of these topics is in-troduced by heuristic order-of-magnituderemarks. Actually, many of these, andmany other heuristic considerations (in partdue to V. Weisskopf) were presented byThirring in a one-semester course entitled‘Unmathematical Physics’ (cf. p. 8). It isa great pity — not only for students! —that this course was given only once andhas never been written up. In contrast,courses along the lines laid down in thefour volumes were given by Thirring regu-larly till the nineties, and many members ofthe Vienna Institute of Theoretical Physicshad the opportunity to give lecture coursesbased on (various parts of) Thirring’scourse at the then recently founded SISSA(Scuola Internazionale di Studi Avanzati)in Trieste during the 1980’s. In fact, this setof courses was included in the SISSA cur-riculum.



Returning to Gravity, it is perhapsneedless to say that there is a continuinginterest on his part in ‘Machian’ matters,in particular in the experimental resultsconcerning the (H.) Thirring-Lense effect.Machian questions were touched upon inthe dissertation of F. Embacher6 underThirring’s supervision. An early question,dating from the fifties, was the discussionof quantum fields in external gravitationalfields; actually, the question came too earlyin the sense that the relevant global as-pects of gravitation, which lie beyond the

domain of the linear approximation, wereunknown or unnoticed at the time (like J.Synge’s 1950 analysis7 of the global struc-ture of Schwarzschild spacetime). Thirringonce told us that he had even discussed par-ticle creation by deep gravitational poten-tial wells with A. Einstein — who charac-teristically did not like the idea.

Notes1 W. Thirring, Fortschr. Phys. 7 (1959), 79.

W.Thirring, Ann. Phys. (N.Y.) 16 (1961), 96.2 R. Sexl, Fortschr. Phys. 15 (1967), 269.3 I.E. Segal, Mathematical Problems of Relativistic

Physics, Providence, R.I.: Amer. Math. Soc., 19634 P. Hertel, H. Narnhofer, W. Thirring, Commun.

Math. Phys. 28 (1972), 159.5 W. Thirring, Classical Field Theory. A course in

Mathematical Physics, vol. 2, second edition. NewYork, Vienna: Springer Verlag, 1978.

6 F. Embacher, Machian Effects and Methods of So-lution for Einsteins Field Equations in the Case ofCylindrically Symmetric Stationarily Rotating Matter,University of Vienna, 1980 [in German].

7 J.L. Synge, Proc. R. Irish Acad. A 53 (1950), 83.

Guidelines for Students ofTheoretical PhysicsWalter Thirring

The following notesby Walter Thirringwere handed to stu-dents of his lecturecourse on Theoreti-cal Physics in 1959.The English transla-tion is due to HelmuthUrbantke.

Theoretical Physics has become an extremelybroad field whose mastery presents steadily in-creasing difficulties. It is, therefore, essential totake the most economic path to avoid unneces-sary waste of time. For this reason, in the fol-lowing I shall give some guidelines to help stu-dents find a suitable path through the jungle ofmodern Theoretical Physics.

1. Tools and Aids

For the understanding of Theoretical Physics,some aids from other parts of science areneeded. Since the material is presented in amathematically deductive manner, knowledgeof mathematical language is indispensable; buteven knowledge does not suffice — it is mas-tery of mathematical techniques that enables in-dependent work. Mainly the following branchesof mathematics are needed:

a) Linear algebra (vectors and tensors)b) Differential and integral calculusc) Differential and integral equationsc) Complex analysis

This material has to be acquired by the studentfrom lectures and suitable textbooks.Furthermore, in Theoretical Physics educationin experimental and general physics is required.This will be, in the first place, knowledge ofphenomena and of related terminology. Thereare lecture courses on these as well as techni-cal literature. Since a large part of the latter is

written in English, knowledge of the latter islikewise needed urgently. To people who wantto engage in Theoretical Physics as a profes-sion, active collaboration in experimental workis strongly recommended. All this knowledge istaken for granted in Theoretical Physics, and inlectures one cannot go into details about it.

2. General Advice

While studying Theoretical Physics, everybodywill go through a few growing pains which arenot to be taken too seriously; but it will be wellto be informed about them. In the following, wewill give a few words of advices in this respect.To the beginner, combination of mathematicalformalism and physical ideas is alien, and it willbe important to be clear about significance andorder of magnitude of the symbols at each stepof calculation. One should believe to have un-derstood a result only if one is able to reproducefrom memory all the steps involved in its deduc-tion. It is not sufficient to be able to follow thesesteps by reading them. To counter these difficul-ties, the following are useful:a) DiscussionsAn essential means to convince oneself of hav-ing reached understanding is discussing it withothers. It is only if one has an overview of ob-jections and suggestions of different kinds thatone may judge the soundness of one’s own ap-proach. In discussions, all shyness and vanitymust be overcome, and one must not be con-tent before the objective state of affairs has beenhonestly ascertained. . . . It is also strongly rec-ommended to physics students to attend semi-nars, because there will be more room for dis-cussions and questions than during the lecturecourses. In particular, PhD students of Theoret-ical Physics should, besides their work on theirtheses, participate in those seminars on princi-ple.b) ExercisesThe execution of typical exercises and problemsis as important for the physicist as is exercis-ing for the pianist. This is why lectures are ac-companied by problem sessions. It is not suf-ficient to calculate and calculate until some re-sult is produced: a major part of the labour has

to be invested into ascertaining the correctnessof the result and discussing its significance. Onthe one hand, one should deduce the result bydifferent methods, pondering about the most di-rect one. On the other, one must inquire aboutthe physical significance and order of magni-tude of the result; by plausibility considerations,one should see the approximate validity of theresult. A frequent mistake is to write down a re-sult with many decimal places without makingsure that the very first decimal place is correct.

c) Lectures

One recommended way — but not the only one— is to attend lectures; one should be careful,however, not to attend too many of them, sinceit is impossible to digest fully more than twoor three per day. Nevertheless, it is recommend-able to work through a subject following a lec-ture course even if one knows it already. In gen-eral, one gets an overview of a subject only iflight is shed upon it from different angles, i.e., ifone has encountered it both in lectures and text-books. Just taking notes from a lecture course isnot sufficient; one must be able to reproduce thematerial from memory.

d) Literature

For most parts of physics, there are excellenttextbooks that enable one to work through thematerial. However, these books cannot be readlike newspapers to be useful, but only with pa-per and pen, so that one may perform all cal-culations oneself. There are many books whosereading is dangerous for beginners. In part, theyare out of age, so that notation, presentation andcontent do not any more correspond to contem-porary knowledge. Also, many books by famousscientists contain suggestions which later turnedout to be useless: studying them means waste oftime without much gain . . .The notes end with a list of recommendedand not recommended textbooks. Among thetextbooks which were not recommended wasArthur Stanley Eddington’s ‘Fundamental The-ory’ and Arnold Sommerfeld’s ‘Atombau undSpektrallinien’ (out of date) and, generally, alltextbooks without new editions after 1930.



Walter Thirring: Probingfor StabilityHarald A. Posch

Almost 40 years ago,Walter Thirring, thenmember of the board ofdirectors at CERN inGeneva, faced a para-doxical problem: as-tronomers had knownfor almost 100 yearsthat extracting energy from a star, for ex-ample by radiation, would make it col-lapse and heat it up. V.A. Antonov evenshowed in 1962 that no equilibrium statewith a global maximum of the Boltzmannentropy exists for a sufficiently large sys-tem of point particles interacting with a1/r potential. This means that the parti-cles form a cluster and continue to col-lapse for ever with their temperature di-verging to infinity, even if the total en-ergy is constant. The British astronomer D.Lynden-Bell realized that an explanationof this so-called gravothermal catastrophein thermodynamic terms requires the spe-cific heat (or more correctly the heat ca-pacity) to become negative. The paradoxwas that physicists “knew” that the specificheat of ordinary matter could be expressedin terms of the square of the energy fluc-tuations and, as a consequence, had to bepositive. Walter, at about the same time andindependent of Lynden-Bell, realized thesignificance of the negative specific heatand “risked his reputation” (in the wordsof the editor), when he published an articlein 19701 in which he explained the differ-ence and resolved the paradox: physicistswere used to specifying the state of matterby the temperature in contact with a heatbath and, hence, within the framework ofthe canonical ensemble. There, the specificheat is indeed always positive. Stars andstar clusters, however, may be consideredas isolated objects with constant total en-ergy, for which the microcanonical ensem-ble provides the proper setting. And therethe specific heat may become negative, de-pending on the particle interaction and theenergy. This provided the first significantexample in statistical mechanics for the re-sults of different ensembles to disagree.

The problem of negative heat capac-ity has continued to interest Walter eversince. Most notably, he showed that neg-ative specific heat is related to other no-tions of stability, namely i) extensivity (sta-bility against implosion), ii) subadditivity(stability against explosion), and iii) con-

vexity of E(S) (thermodynamic stability).According to a theorem by Walter Thirring,the three stability conditions are intimatelyconnected: each pair of conditions impliesthe third.2

The dynamics of thermally unstablesystems has also provided the backgroundfor my collaboration with Walter up to thepresent day. Earlier than most theoreticalphysicists, he accepted computer simula-tions of complex dynamical events as a le-gitimate tool to check and guide the intu-ition and to study systems still outside ofpresent-day theory. In 1989, in collabora-tion with H. Narnhofer, we conducted a se-ries of computer simulations with a sim-plified model of 400 particles in a box in-teracting with a short-ranged attractive po-tential.3 We established the unusual ther-mal properties of negative specific heat ina certain range of energies and studied theparticle-number dependence. As an exam-ple, in Figure 1 a typical particle clusteris shown, which forms after the simulationhas been initiated with a homogeneous gas.

FIGURE 1: 400 ATTRACTING PARTICLES IN BOX.

CONFIGURATION AT A TIME t0 = 3000. THE PARTICLES

ARE REPRESENTED BY CIRCLES WITH DIAMETER EQUAL

TO THE INFLECTION POINT OF THE NEGATIVE GAUSS

POTENTIAL.

By coupling to a heat bath, we also ex-plicitly demonstrated that the negative heatcapacity disappears and is replaced by afirst-order clustering phase transition whenthe simulations are carried out within thecanonical ensemble.4

The next logical step with such an un-familiar matter was to check for the Sec-ond Law. We performed a computer exper-iment of an adiabatic cyclic process, wherethe volume of the box was periodically ex-panded and contracted, reducing and rais-ing the energy in the process.5 During theexpansion the cluster formed and disap-peared again during compression. The neteffect always was an increase of the sys-tem’s energy, which excludes the possibil-ity of a perpetuum mobile of the second

kind. The coarse grained entropy increasedboth during the expansion and compres-sion, but only when it was of the Boltz-mann type. Other entropies with coarsegraining solely in the momentum or con-figuration space failed the test. Using theconcept of passivity, Walter also demon-strated, for an ensemble of harmonic os-cillators with periodically-switched forceconstants, that active states, which violatethe Second Law, are located on a fractal setin phase space with a measure which van-ishes in the many-particle limit.

But a star is threatened not only by thegravothermal effect, which would cause itto implode and heat up in the process. Itis also subjected to a second gigantic in-stability, the thermonuclear heating in it’score. The later which would cause it to ex-plode if unchecked. Both instabilities, thegravothermal effect and thermonuclear en-ergy input, are intimately linked togetherand neutralize each other for billions ofyears. The negative heat capacity changesthe bifurcation point due to exponentialnuclear energy input and radiative energylosses into a fixed point. But beware, ifeventually one of the gigantic instabilitiesgets weaker than the other! Recently, weexhibited this delicate balance with twosimple examples.6 The first is the many-body system of Figure 1. If energy is addedto the equilibrated particles in the maincluster for times t > 3000, the tempera-ture of the cluster particles goes down asdepicted by curve B in Figure 2.

FIGURE 2: TIME EVOLUTION FOR THE TEMPERATURE Tc

OF THE LARGEST CLUSTER. LINE A BELONGS TO THE

EQUILIBRATION STEP, LINE B TO THE HEATING STEP, AND

LINE C TO THE FINAL HEATING/COOLING STEP.

If, in addition to heating the cluster par-ticles, the system is also subjected to acooling process at the boundary supposedto mimic radiation loss off the star, the tem-perature goes up again until it reaches a sta-tionary state. This is shown by curve C inFigure 2. This provides a beautiful examplefor the mutual stabilizing effects of the twootherwise destructive phenomena.

The second model emphasizes anotherinteresting observation:7 negative specific



heat means that the volume of the energyshell expands more than exponentially withenergy. In gravity-dominated systems theformation of clusters always causes heat-ing, that is expansion in momentum space.If, however, more than exponential expan-sion is provided in configuration space, thesystem may even cool down and still shownegative specific heat. The model Walterproposed is shown in Figure 3.

FIGURE 3: JUMPING BOARD MODEL AND SHORT CHAOTIC

TRAJECTORY FOR A PARTICLE. THE GRAVITATIONAL

FORCE POINTS INTO THE NEGATIVE y DIRECTION. AT

THE BOTTOM, THE PARTICLE IS ELASTICALLY

REFLECTED. TO AVOID NEGATIVE x, THE y AXIS ACTS AS

AN ELASTIC MIRROR.

A particle, or an ensemble of weakly inter-acting particles, is subjected to a gravita-tional field parallel to the negative y axisand confined to a valley, which opens upvery quickly such that the accessible con-figuration space increases faster than ex-ponentially with the energy (respective themaximum height the particle may jump to).The farther the particle gets to the rightin this way, the more potential energy isused up and the colder the particle gets,a clear sign of negative specific heat. Thenon-equilibrium version of this model (theparticles farthest to the right are allowedto fall out of the potential well) may alsobe looked at as the most-efficient form ofevaporation cooling, a process extensivelystudied to generate ultra-cold gases in con-nection with Bose-Einstein condensation.

This simple model is also the first me-chanical device with negative specific heat,which could be built in the laboratory, atleast in principle.

The gravitational collapse of a few par-ticles in a box due to the gravothermal ef-fect may also be prevented, if the particlesare subjected to external constraints, whichreduces the allowed phase space such thatthe system asymptotically remains stable.We studied, for example, what effect mo-mentum and/or angular momentum conser-vation has on such a system. Three particlesin a square box in two dimensions will col-lapse for ever, in a circular box the collapsecomes to an end in a finite time due to an-gular momentum conservation present onlyin this case.8

Recently, the problem of negative heatcapacity was front-page news again, whenlaboratory experiments on nuclear frag-mentation and atomic clusters hinted tothe existence of this phenomenon alsofor ordinary Coulombic matter, for whichgravitation could not be the culprit. Thisseemed to contradict a general result byJ. L. Lebowitz and E. H. Lieb accordingto which a quantum-mechanical Coulombsystem consisting of electrons and nu-clei always has positive specific heat,even in the microcanonical ensemble. Ofcourse, this theorem presupposes ergodic-ity and the thermodynamic limit. We coulddemonstrate by computer simulations andsimple model calculations that the failureof any of the two assumptions may be suf-ficient to render the specific heat negativein some restricted range of energy.9

I had the good fortune to study manyother problems with Walter. I would like tomention the problem of ergodicity and theLyapunov instability of one-dimensionalgravitational systems,10 the unpredictabil-ity of symmetry breaking in phase tran-sitions,11 and some aspects of the clas-

sical three-body problem.12 The work onthese problems always brought to light thedeep intuitive insight Walter has of thephysical world, which is rivalled only byhis extraordinary mathematical skills hebrings up when solving a problem. As be-fits a great physicist, most recently Wal-ter Thirring has turned also to another out-standing problem, the study of evolutionaryprocesses leading to the formation of struc-tures, to the selection of species. Again, thecomputer turns out to be an invaluable tooland provides the opportunity for me to par-ticipate in this adventure.13 For this, andfor his generosity in all scientific and pri-vate matters I am forever grateful.

Notes1 W. Thirring, Z. Physik 235 (1970), 339.

P. Hertel and W. Thirring, Ann. Phys. 63 (1971),520.

2 W. Thirring, Quantum Mathematical Physics,2nd edition, Springer Verlag: Berlin, 2001.

3 H.A. Posch, H. Narnhofer, and W. Thirring, Phys.Rev. A 42 (1990), 1880.

H.A. Posch, H. Narnhofer, and W. Thirring,Microscopic Simulations of Complex Systems, M.Mareschal ed., New York: Plenum Press, 1990, p. 241.

4 H.A. Posch, H. Narnhofer, and W. Thirring, Phys-ica A 194 (1993), 481.

5 H.A. Posch, H. Narnhofer, and W. Thirring, J.Stat. Phys. 65 (1991), 555.

6 H.A. Posch and W. Thirring, Phys. Rev. Lett. 95(2005), 251101.

7 H.A. Posch and W. Thirring, Phys. Rev. Lett. 95(2005), 251101.

H.A. Posch and W. Thirring, Phys. Rev. E 74(2006), 051103.

8 Lj. Milanovic, H. A. Posch, and W. Thirring, J.Stat. Phys. 124 (2006), 843.

9 W. Thirring, H. Narnhofer and H.A. Posch, Phys.Rev. Lett. 91 (2003), 130601.

10 Lj. Milanovic, H. A. Posch, and W. Thirring,Phys. Rev. E 57 (1998), 2763.

Lj. Milanovic, H. A. Posch, and W. Thirring, J.Stat. Phys. 124 (2006), 843.

11 H.A. Posch and W. Thirring, Phys. Rev. E 48(1993), 4333.

12 H.A. Posch and W. Thirring, J. Math. Phys. 41(2000), 3430.

13 Ch. Marx, H.A. Posch and W. Thirring, Phys.Rev. E, in press (2007).

Almost 50 Years of theThirring ModelHarald Grosse

The formulation ofrenormalized perturba-tive quantum field the-ory by Dyson, Feyn-man, Schwinger andTomonaga predictedobservable correctionsdue to quantum fluc-

tuations, which are confirmed by experi-ments to an extremely high precision. After

the construction of a solvable field theoryby Lee many people tried to obtain a simi-lar relativistic model too. The well knownBethe Ansatz, successfully applied in thethirties to the Heisenberg chain model,served as a guide.

Heisenberg proposed in the fiftiesa Four-Fermi Interaction Model (‘Ur-formel’), which, as was noticed immedi-ately by Pauli, led to difficulties, since it isnot renormalizable.

The analogous two-dimensional model,formulated already by Tomonaga in theearly fifties, was studied by Walter Thirringand published 1958. With the help of

the Bethe-Ansatz he was able to solvethe appropriate many particle system ina Hilbert Space of fixed particle number.The next step to change the representationfor which the spectral condition is fulfilledneeds renormalization and is tricky. Withinthe physical correct representation Thirringwas able to calculate the two particle cor-relation function with one particle on shell,which is called the form factor.

Soon after this work Glaser proposedan operator solution to the model and ob-tained surprisingly for the form factor ananswer which differed from Thirring’s an-swer by a change of coupling constant.



This puzzling situation was analyzed by anumber of people like Johnson, Klaiber,Wightman and others from various pointsof view. Nowadays, of course, it is easyto state that only renormalized quantitiesmake sense and the step from bare to renor-malized ones depends on the renormaliza-tion scheme. Klaiber wrote down a gener-alized solution of the massless model.

In 1962 Schwinger extended the setof solvable models. Two-dimensional QEDshows mass generation and appearance ofa theta vacuum. It was a common effortof many physicists and mathematicians, es-pecially Australians around Carey, to es-tablish Wightman axioms for these mod-els. Two-dimensional conformal field the-ory ideas can be tested again on the mass-less model and allow for many generaliza-tions.

Of course, nowadays, an infinite num-ber of solvable, respectively almost solv-able integrable models are known and stud-ied in detail. Especially the algebraic struc-ture behind the Yang-Baxter equation ledto the invention of quantum groups whichgeneralize the Lie algebra structure.

Despite many attempts (also by my-self), the massive Thirring model resists acomplete solution. Assuming factorization,

unitarity, crossing and no particle creationit was possible to deduce a possible S-matrix. Again it was possible to obtain theform factor, but no higher correlation func-tions have been obtained in closed form.On the other hand from constructive meth-ods the existence of these higher correla-tion functions has been derived.

Coleman’s duality allows to map themassive model to the Sine-Gordon modelwith all its solitons, antisolitons andbreathers. This generalized the Kramers-Wannier duality of the Ising model sub-stantially, and was extended through workof Olive-Montonen and many others tothe fascinating geometric Langlands dual-ity concept, which became popular recentlythrough work of Kapustin and Witten. Suchunforeseen developments show the powerof toy models which seem to be unphysi-cal at first sight, but allow to study physicaleffects in a nutshell.

The completely independent develop-ments (almost at the same time) in sta-tistical physics are worth mentioning. Thewell-known Luttinger model represents akind of lattice-regularized Thirring model,were renormalization effects can be stud-ied easily. Its first correct solution is dueto Mattis and Lieb. Its physics implications

are nowadays well established: conductiv-ity along one-dimensional quantum wiresis well described by the Luttinger liquid.

It is interesting to note that the twomain proponents of these developmentsin two different fields, in two-dimensionalquantum field theory and two-dimensionalstatistical physics, joined and obtained asubstantial improvement of the stability ofmatter proof of Dyson-Lenard. AlthoughThirring’s calculation of the distribution ofpressure of teeth might be of more prac-tical importance, the first analysis of thetwo-dimensional spinor model gave a greatimpulse and led to many generalizations.The still puzzling situation of the four-dimensional local or even nonlocal quan-tum field theory models forces us evennowadays to study toy models in lower di-mensions.

During the almost 50 years which havepassed since the first study of the mass-less Thirring model, it has served as atoy model and a testing ground for gen-eral ideas and phenomena. A similar four-dimensional model is still to be discovered;the best candidates are N = 4 or evenN = 8 supersymmetric models.

A Crossword PuzzleWithout Clues1

Can one find a ‘Theory of Everything’by pure thinking?Peter C. Aichelburg

I dedicate this article to my teacher Wal-ter Thirring who not only introduced me tomodern theoretical physics, but also guidedmy scientific interest towards Relativity.

Modern theoreticalphysics is confrontedwith a dilemma. Thestandard model ofparticle physics is inexcellent agreementwith experiments andEinstein’s theory ofgravitation is confirmed every day whenapplied to the satellites of the global po-sition system. However, the decisive steptowards a complete theory describing ourphysical world is missing: the unificationof quantum theory and gravitation. Thedilemma is that nature does not seem togive us any clue how to achieve this.

It is fair to say that, over the pastdecades, the brightest scientists in the fieldhave devoted their efforts to this question.

A number of challenging ideas are on thescientific market, especially modern stringtheory which tries to unify all fundamen-tal forces. But string theory has recentlycome under severe criticism, even from ex-perts in the field. The problem is experi-mental verification: although most of theseproposed theories may be falsified in prin-ciple in the sense of Popper, any of theirexpected consequences are far too small fortoday’s methods of detection.

Revolutions in physics were almostalways triggered by observations whichwere either in conflict with, or could notbe explained by, current theories. For ex-ample, the emission of electromagneticwaves with definite frequencies by atomswas in contradiction with classical electro-magnetic theory and led to the formula-tion of quantum theory, forcing physics toabandon a deterministic description of theworld.

Today, however, the situation is differ-ent. Since there are no observations whichare in contradiction with the establishedtheories, an essential guiding principle isabsent. The problem may be compared toa crossword puzzle without clues, where itis difficult, but not impossible to solve thepuzzle. The only guideline is internal con-

sistency i.e. that the letters at the intersec-tions of words must agree. Moreover, thepuzzle should admit only a single correctsolution.

If this argument were to be applied tothe physical description of the word wecould do away with the sophisticated ex-periments in particle physics and costlylarge telescopes for astronomers. All thatwould be needed are mental efforts of the-oreticians.

In fact, never before have so many sci-entists dedicated themselves to the con-struction of theories which are far beyondany observational verification, the only cri-terion being internal consistency and con-vergence to existing theories when takingsuitable limits. However, in pursuing theanalogy with a crossword puzzle a littlefurther, an essential feature of the problemis missing. Even if the solution is uniqueit can only be found if the number of‘squares’ in the puzzle is finite. An infi-nite puzzle can not only not be solved com-pletely, but unfortunately also not partially.It may happen that one has found a con-sistent solution of, say, the upper left cor-ner, but that one runs into contradictions ata later stage. This forces one to go back andabandon what has already been obtained. If



the puzzle is unbounded, this may happenagain and again at every stage.

Without no generally accepted the-ory at hand it is not too astonishing thatsometimes the fantasies of scientists goastray. Every now and then the public isconfronted with new and surprising ideasabout the origin of the universe. For exam-ple, that our cosmos is the result of a vac-uum fluctuation and that these processestake place continuously and our world istherefore just one in an infinite ‘multi-verse’. Or that we live on a kind of mem-brane embedded in a higher–dimensionalspace, where the extra dimensions mani-fest themselves purely through the forceof gravity. If one follows the well knownphysicist Lee Smolin in his book The Lifeof the Cosmos2 one learns that for the uni-verse a cosmological natural selection actssimilarly to biological evolution.

What should we think of such ideas?Without doubt, there is today not a sin-gle observation which supports these spec-ulations. In contrast, the Nobel Price 2006in Physics was awarded to the Americanscientists John Mather and George Smootfor the detection of the structure and exactform of the cosmic microwave background.These observations give strong support tothe big bang theory. They show a detailedpicture of the universe of more than 13 bil-lions year ago and made cosmology a pre-cise science.

How do these observations compare toclaims made about the emergence of ourcosmos? We are confronted with a ques-tionable embellishment of observation–supported knowledge on the one side, andwith imaginative speculations on the other.Such speculations reach the public throughpopular and semi-popular books and areapparently well received. In our secular-ized world, where an increasing number ofpeople find it difficult to unite ‘rationality’and ‘religious faith’, such concepts take the

place that traditionally was provided by re-ligious genesis. Religious faith is replacedby scientific faith. But only few are awarethat the scientific basis of these statementsis rather meagre.

Not trying to make a case for intel-ligent design, it is fair to say that up tonow there does not exist a theory whichwould allow us to model the beginning ofthe universe. Einstein’s theory of GeneralRelativity gives a dynamical description ofthe cosmos as a whole, but shows at thesame time its limits of applicability. Thebig bang, where the density of the substratethat fills the cosmos increases unbound-edly, thereby driving the geometry into asingularity, lies outside the scope of thetheory. The theory cannot make statementsabout the big bang itself.

To overcome this problem one wouldneed a theory which unites Einstein’s grav-ity with quantum theory, the theory thatgoverns interactions at the microscopiclevel. Such a ‘theory of everything’ isthe dream of many physicists. Although itmight be possible to find a unique consis-tent theory of nature by pure thought, it isvery unlikely. Knowledge about our uni-verse has to be based and oriented on ob-servation.

What then is observation–based knowl-edge in modern cosmology? The main as-sertion is that the universe undergoes a con-tinuous change and that it has emergedfrom a dense state about 14 billion yearsago. This big bang theory is supported bythree key observations:

(i) The shift in frequency of light com-ing from distant galaxies which indi-cates that the cosmos as a whole issubjected to a general expansion.

(ii) The cosmic microwave backgroundradiation confirms that the early uni-verse was dense and hot.

(iii) Physicists were able to calculate theformation of the first generation of

light atomic nuclei in the universe.These calculations are based on lawsfor subatomic matter tested in exper-iments at accelerators and reactors.The theory for the primordial nuclearsynthesis turned out to be in excel-lent agreement with observations.

On the other hand there is the seri-ous and so far unsolved problem of darkmatter. As the name says, dark matter cannot be seen directly and its presence issolely noticed through its gravitational ef-fects, e.g. the bending of light rays whichreach us from distant objects. Dark mat-ter must have completely different prop-erties from ordinary matter, otherwise itwould have influenced the primordial dis-tribution of light nuclei. Scientists expectto obtain clues about the strange propertiesof dark matter when the Large Hadron Col-lider (LHC) at CERN in Geneva goes intooperation this year. Still more mysteriousis what is called the dark energy: obser-vations of exploding stars in distant galax-ies indicate that the cosmic expansion isaccelerating, while ordinary matter shouldslow down the expansion rate. These find-ings are also supported by the observed finestructure in the microwave background. In-vestigations indicate the existence of a yetunknown substrate.

It may well be that the search for thisdark energy could give a decisive clue toa connection between the quantum worldof the microcosmos and the largest dimen-sion of the universe dominated by gravity.This could bring the long–lasting search fora theory of quantum gravity back into thestate of an observation–based science.

Notes1 A German version of this article was published in

the Austrian newspaper ‘Die Presse’ on February 16,2007.

2 Lee Smolin, The Life of the Cosmos, Oxford Uni-versity Press USA, 1998.

Doing Physics with WalterElliott Lieb

My scientific life hasnatural dividing lines,like new chapters ina book, the most im-portant of which isthe day I started towork with Walter.Walter says we met

in 1968, and that is undoubtedly true, but

my memory goes back to a turning pointin the early seventies when we were sittingaround a lunch counter somewhere andWalter asked me if I ever thought aboutthe Dyson-Lenard proof of the stability ofmatter. No, I hadn’t really, but he had, andhe realized that, while correct, it neededsome new mathematical insight to make itphysically understandable as well as math-ematically correct.

Walter invited me to be a ‘Schrodingerguest professor’ at the University of Viennain the summer of 1974, and while this visit

led to lots of fruitful scientific discussion(including collaboration with Heide Narn-hofer) nothing dramatic happened exceptthat I lost a key to the Institute. Fortunately,and this must be recorded for posterity, themainstay of Walter’s group, apart, natu-rally, from his wife Helga, was his assis-tant Franziska (Franzi) Wagner. She coulddo everything; not only type up the stuff wegenerated but also figure out how to dealwith a missing, priceless, irreplaceable keythat was official government propoerty andmust never, under any conditions be lost or



duplicated.But to return to the story, I was a

‘Schrodinger guest professor’ again in thesummer of 1975 and this time we solvedthe problem. The main new idea was therealization that the kinetic energy of elec-trons ( and other particles satisfying Pauli’sexclusion principle) is always greater thanthe integral over all space of the 5/3 powerof the particle density. This, in turn, meantthat the old theory of E. Fermi and L.H.Thomas gave a lower bound to the total en-ergy of matter, and this bound was known(by earlier work with Simon) to satisfy thedesired stability condition.

We had several collaborations afterthat, but our last published work togetherwas the proof in 1986 that the attractivevan der Waals force between pairs of atoms

or molecules, which drops off like the neg-ative sixth power of the distance betweenthem (in the absence of electromagneticpropagation corrections), was a universalconsequence of Schrodinger’s equation.

There were enjoyable visits before andafter 1986. I would visit Walter in his hide-away in Zweiersdorf, where Helga was asuperb hostess, and he would often visitmy wife and me in Princeton. Walter isone of the most organized people I know.The visits followed a rigorous time sched-ule starting around 6 am and ending around9 pm that dictated when we would wakeup, take walks, play music, exercise and doscience. Walter is an accomplished pianoand organ player, and composer, while Iwas a fifth rate recorder (Blockflote) player.Following an internal alarm clock Walter

would announce that it was time to stopthe science and play some baroque sonatas,and he would very patiently overlook mymissed entrances and other mistakes. It wasfun and I learned a lot, but I also realizedthat I would never be organized enough todo all the many things, in many fields, thatWalter is capable of doing.

Walter continues his work in sciencewith the energy of a newcomer. Not onlyis he interested in everything but he con-tinues to do original research in his inim-itable style – which is to do what you thinkis interesting and important without payingmuch attention to the fashion of the day.Welcome to the 80’s, Walter, and continueto inspire us youngsters by doing great sci-ence!

Encounters with WalterThirringAngas Hurst

My first contact withWalter was when Isaw a letter in Phys-ical Review in 1950written by him fromDublin. It was prob-ably his first publi-cation and dealt with‘Regularization as a Consequence ofHigher Order Equations’. This was a neatconnection between higher order waveequations and the Pauli-Villars regularisa-tion. This was particularly helpful for mebecause shortly before I had heard Paulideliver the Rouse Ball lecture to the math-ematics faculty in Cambridge, and it wasan example of how not to do things. Onlysomeone with Pauli’s reputation could havegot away with it. He introduced a methodfor controlling divergences in quantumfield theory to a general audience of mathe-maticians who almost certainly knew littleabout quantum field theory and less aboutthe problems of divergences. His deliveryconsisted of walking backwards and for-wards in front of the audience, with hishead sunk on his chest, accompanied bya regular squeak of a loose floorboard inthe middle of his to and fro path. As abarely beginning research student I wascompletely lost. So Walter’s paper was alight in the darkness.

Later on we had a more personal en-counter when he wrote to me about thecontent of my PhD thesis on the conver-gence of the quantum field theory pertur-

bation expansion. Apparently he had beeninstructed by Pauli to check it out as itmade some rather strong assertions. Notonly did he check it out, but he rederivedthe results by much neater methods andcompleted the outstanding gap of includ-ing renormalisation effects. As a result thequantum field used was called, by Bogoli-ubov and Shirkov, the Hurst-Thirring field,and so our names have always since thenbeen coupled together, although our pathshave diverged widely.

Walter became one of the stalwarts ofEuropean physics, whilst I led a somewhatquieter life bringing mathematical physicsto Australia, carrying on a tradition startedin Adelaide University by William Bragg,and it was not until I went to a Summer Re-search Institute at Hercegnovi in 1961thatwe actually met. I went as someone whowanted to catch up after nearly a decade ofisolation in Adelaide, and Walter was thereas one of the lecturers. It was a very dis-tinguished gathering, both for the standingof the lecturers and for the collection ofstudents, many of whom became world fa-mous. Apart from the lectures, Walter spentmost of his time drifting around the lovelyharbour using a snorkel, and I broughtsome order in the Proceedings by correct-ing much of the distorted European Englishprovided by the lecturers. The final distinc-tion of this meeting was that Walter invitedme to come to Vienna, where I gave a sem-inar on work I had done with Green on theIsing model. It was also a marvellous op-portunity to see Vienna, and to enjoy itswonderful music and art galleries.

Since then I have been to Vienna onnumerous occasions and Walter and Helgacame to Australia in 1987, staying with

us in Adelaide for two weeks. During thattime we took them to visit the propertyof a former mathematical physics student,which occupied 200 square miles, and wascomplete with shearing sheds and kanga-roos. As a result they became great loversof Australian television series.

Two areas in which our interests haveoverlapped have been in physical systemsin which C∗-algebras have been a potentmethod.

The first was a paper with Heide Narn-hofer on the construction of covariant QEDwithout an indefinite metric. This thinkingclosely parallels work that I did in collabo-ration with Alan Carey, Janice Gaffney andHendrik Grundling, which took off froman old paper I wrote in 1960. Our finalconclusion was that for gauge field theo-ries, or more generally theories with non-integrable constraints, a very wide range ofrepresentations may be employed so longas the observable part is treated by a regu-lar Hilbert space representation. What onedoes with the non-observable part does notmatter, so indefinite metric or nonseparablerepresentations or other pathologies can beemployed without prejudice. For this C∗-algebraic methods are crucial, which Wal-ter and Heide spelt out very thoroughly fortheir system.

The second area is in a very deep studyof the description of entropy in operator al-gebras, and it touches on a question, whichhas bothered me for years, which is how tounderstand the way in which informationis parcelled between physical theories andraw data. I am bothered by a remark I oncesaw Paul Davies makes about complexityof systems, and how theoretical science hasbeen able to succeed because it has been



possible to shunt the complexity into thedata, whilst still having manageable theo-ries. This seems to be a gift which Nature

has made us, and it need not have been so.I shall continue to admire the depth and

diversity of Walter’s work, and I am very

privileged to have had so valuable a friend-ship.

Birthday Greetings toWalter ThirringErnest M. Henley

I have known WalterThirring for over 50years. Walter used tocome to the Univer-sity of Washington dur-ing summers, which isthe nicest time of yearhere. We had Theoreti-cal Summer Institutes, organized by a col-league (Boris Jacobsohn) and me, with thehelp of members of the Physics Depart-ment. These Institutes attracted quite a fewwell known physicists, as well as youngerones, to the University. During one of thesummers in the late 1950’s, Walter gave aseries of lectures on quantum field theoryand exactly soluble models in it. The lec-

tures were excellent. Walter conceived theidea of publishing these lectures and askedme whether I would be willing to collabo-rate. I was eager to do so. After we wrotethe lectures up, we asked students to finderrors and offered monetary rewards. Still,after the book was published as Introduc-tion to Quantum Field Theory by McGraw-Hill we continued to find errors which hadeluded both the students and us. I noted allof these errors in my copy. When McGraw-Hill asked to borrow the annotated copy fora translation into Japanese, I agreed, withthe proviso that the book would be returnedto me. Unfortunately, I never saw the bookagain, and McGraw-Hill could not locateit! By then, the book was out of print. Sincethis was before Xerox was popular, I, un-fortunately, had not copied the corrections.

The book is only one of many pleas-ant memories of the Thirrings’ visits. Wewent on many hikes together. I particu-larly remember one notable one to the top

of Mt.Dickerman. The mountain was en-veloped in fog, but we thought that it wouldclear or that the top would be out of thefog. Instead, the fog got worse and worsethe higher we went. Fortunately, there isa well known blueberry area about 3/4 ofthe way up, where we gorged ourselves andhad lunch. On top, you could barely seeyour own feet. Nevertheless, I pointed outall the wonderful peaks that you could see(on a clear day): Glacier Peak, Sloan peak,Big Four, Vesper, and Monte Cristo, amongothers. It is such a beautiful sight that Iwas deeply sorry that Walter and Helga hadmissed out! We never managed to repeatthis hike.

We have remained good friends overthe years. Whenever I can get to Vienna Ido so and always visit the Thirrings.

My best wishes to Walter on his 80thbirthday. I wish I could attend the sympo-sium and the celebration.

ESI NewsThe ESI Junior Research Fellows Pro-gramme (ESI-JRF) has been extended bya further three-year period (2007 – 2009).

Funded by the Austrian Ministry of Sci-ence and Research, the programme pro-vides support for PhD students and youngpost-docs to participate in the scientific ac-tivities of the Institute and to collaboratewith its visitors and members of the localscientific community for periods between2 and 6 months.During the initial three-year period (2004 –2006) the ESI-JRF programme establisheditself as a highly successful component ofthe Institute’s scientific activities. Both thenumber and quality of the applicants ex-ceeded all expectations, and only 66 outof 282 applications could be funded duringthe years 2004 – 2006, although about 70% of the applicants were judged to be of‘supportable’ standard.In 2004, the level of funding of the pro-gramme had been set at e 150.000/year.In 2005 funding was increased toe 200.000/year, with the additionale 50.000 earmarked to help increase thepercentage of women engaged in mathe-matical research.Although we have not been given precise

figures yet, the funding level of the pro-gramme for 2007 – 2009 is expected to beat least e 200.000/year.Currently there are 7 post-docs at the ESI, 6of whom are funded by the Junior ResearchFellows programme.The most recent call for applications endedon April 30, 2007, and attracted 37 appli-cations.The deadline for the next round of appli-cations for ESI Junior Research Fellow-ships will be November 10, 2007.

In the ESI Senior Research Fellows Pro-gramme the following courses will be of-fered during the Summer Term 2007 andthe Winter Term 2007/08.

Summer Term 2007

• Vadim Kaimanovich, InternationalUniversity Bremen: Boundaries ofgroups: geometric and probabilisticaspects.

• Miroslav Englis, Academy of Sci-ences, Prague: Analysis on complexsymmetric spaces.

• Thomas Mohaupt, University of Liv-erpool: Black holes, supersymmetryand strings (Part II).

Autumn/Winter Term 2007/08

• Christos Likos, Heinrich-Heine Uni-versity, Dusseldorf: Theory of softmatter.

• Radoslav Rashkov, Sofia University:Dualities between gauge theoriesand strings.

For further information concerning thecontents of these lecture courses and rel-evant literature we refer to the web pagehttp://www.esi.ac.at/activities/courses.html.

The European Post-Doctoral Institute(EPDI): The European Post-Doctoral In-stitute for Mathematical Sciences wasfounded in October 1995 with the ambi-tion of facilitating the mobility of youngscientists within Europe. The Institut desHautes Etudes Scientifiques (Paris), theIsaac Newton Institute for Mathemati-cal Sciences (Cambridge) and the Max-Planck-Institut fur Mathematik (Bonn) asfounding members were later joined byseveral other institutes, among them theErwin-Schrodinger Institute. This initiativeturned out to be a very successful scien-tific enterprise which enabled young re-searchers to pursue their work at the partic-ipating institutions. This January, the 12thcall came to a conclusion in a meeting



of the Scientific Committee at the Mittag-Leffler Institute Stockholm, where the win-ners of the two-year research fellowshipsfor the period 2007-2009 were nominated.It is worth noting the number of womenelected is very high compared to the num-ber within the scientific community.

In January 2007, Klaus Schmidt gave a

PIMS 10th Anniversary Distinguished Lec-ture with the title ‘On some of the differ-ences between Z and Z2 in dynamics.’

In December 2006, Jakob Yngvason heldthe Erwin Schrodinger Lectures at the Uni-versity Colleges in Cork and Limerick andat Trinity College, Dublin, Ireland. This an-nual lecture series, supported by the Aus-

trian Embassy in Dublin and the NationalBank of Austria, commemorates the fa-mous lectures ‘What is life’ given by ErwinSchrodinger at Trinity College in 1943.Jakob Yngvason also gave the Andrejew-ski Lectures at the University of Leipzig inJanuary 2007.

Current and Future Activities of the ESI

Thematic Programmes

Amenability, February 26 – July 31, 2007.

Organizers: A. Erschler, V. Kaimanovich, K. Schmidt

Workshop on amenability beyond groups, February 26 – March17, 2007

Workshop on algebraic aspects of amenability, June 18 – June30, 2007

Workshop on geometric and probabilistic aspects ofamenability, July 2 – July 14, 2007

Poisson Sigma Models, Lie Algebroids, Deformations andHigher Analogues, August 1 – September 30, 2007

Organizers: H. Bursztyn, H. Grosse, T. Strobl

Applications of the Renormalization group, October 15 –November 25, 2007

Organizers: G. Gentile, H. Grosse, G. Huisken, V. Mastropietro

Workshop on the Renormalization Group Flow and Ricci Flow,October 22 – 26, 2007

Workshop on Renormalization in Dynamical Systems, October29 – November 3, 2007

Workshop on Renormalization in Quantum Field Theory,Statistical Mechanics and Condensed Matter, November 12 – 17,2007The programme will be followed by an ESF-Workshop onNon-commutative Quantum Field Theory, November 26 – 30,2007. Introductory courses to this subject will be given by J. Barrettand R. Szabo in the week November 19 – 23, 2007.

Combinatorics and Statistical Physics, February 1 – June 15, 2008

Organisers: M. Bousquet-Melou, M. Drmota, C. Krattenthaler, B.Nienhuis

Workshop, May 25 – June 7, 2008

Summer School, July 7 – July 18, 2008

Metastability and Rare Events in Complex Systems, February 1– April 30, 2008

Organizers: P.G. Bolhuis, C. Dellago, E. van den Eijnden

Workshop, February 17 – February 23, 2008

Hyberbolic Dynamical Systems, May 12 – July 5, 2008

Organisers: H. Posch, D. Szasz, L.-S. Young

Workshop, June 15 – June 29, 2008

Operator Algebras and Conformal Field Theory, August 25 –December 15, 2008

Organisers: Y. Kawahigashi, R. Longo, K.-H. Rehren, J. Yngvason

Other Scientific Activities

First European Young Scientists Conference on QuantumInformation, August 27 - 31, 2007

Organizers: Simon Groblacher and Robert Prevedel

Central European joint Programme of Doctoral Studies inTheoretical Physics, September 24 - 28, 2007

Organizer: Helmuth Huffel

There will be two lecture courses of 15 lectures each:Harald Grosse: Noncommutative Quantum Field TheoryJakob Yngvason: Local Quantum Physics

Fourth Vienna Central European Seminar on Particle Physicsand Quantum Field Theory, November 30 – December 2, 2007

Theme: Commutative and Noncommutative Quantum Field theory

Organizer: Helmuth Huffel



ThirringfestTuesday, May 15, 2007

Lecture Hall of the Faculty of Physics, Strudlhofgasse 4, 1090 Vienna

10:00 – 10:15 Welcome addresses

GEORG WINCKLER, Rektor, University of ViennaANTON ZEILINGER, Dean, Faculty of Physics, University of ViennaKLAUS SCHMIDT, President, ESI

10:15 – 11:15 Wolfgang Rindler (Dallas): Vienna, Hans Thirring, and Gravity Probe B

11:15 – 11:45 Coffee Break

11:45 – 12:45 Julius Wess (Munich): Deformed Theory of Gravity

14:30 – 15:30 Elliott H. Lieb (Princeton): Remarks on Density Functional Theory

17:30 – 18:30 Eine kleine Hausmusik: Chamber music composed by Walter ThirringPerformed by friends at Pfarrsaal, Nussdorf, Pfarrplatz 3, 1190 Wien

19:00 – Heuriger – Maier am Pfarrplatz

Editors: Klaus Schmidt, Joachim Schwermer, Jakob Yngvason

Contributors:Peter C. Aichelburg: [email protected] Baumgartner: [email protected] Grosse: [email protected] M. Henley: [email protected] Hurst: [email protected] Kummer: [email protected] Lieb: [email protected] Narnhofer: [email protected] Pietschmann: [email protected] A. Posch: [email protected] L. Reiter: [email protected] Thirring: [email protected] Urbantke: [email protected]

ESI Contact List:AdministrationIsabella Miedl: [email protected]

Scientific DirectorsJoachim Schwermer: [email protected] Yngvason: [email protected]

PresidentKlaus Schmidt: [email protected]

The ESI is supported by the Austrian Federal Ministry for Science and Research ( ). The ESI Senior Research FellowsProgramme is additionally supported by the University of Vienna and the Vienna University of Technology.

This newsletter is available on the web at: ftp://ftp.esi.ac.at/pub/ESI-News/ESI-News2.1.pdf

IMPRESSUM: Herausgeber, Eigentumer und Verleger: INTERNATIONALES ERWIN SCHRODINGER INSTITUT FUR MATHEMATISCHE PHYSIK, Boltzmanngasse 9/2, A-1090 Wien.

Redaktion und Sekretariat: Telefon: +43-1-4277-28282, Fax: +43-1-4277-28299, Email: [email protected]

Zweck der Publikation: Information der Mitglieder des Vereins Erwin Schrodinger Institut und der Offentlichkeit in wissenschaftlichen und organisatorischen Belangen. Forderung der

Kenntnisse uber die mathematischen Wissenschaften und deren kultureller und gesellschaftlicher Relevanz.


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