INTRODUCTION TO QUANTUM FIELDdownloads.hindawi.com/archive/1997/298275.pdf · 2019-08-01 ·...
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Journal of Applied Mathematics and Stochastic Analysis, 10:1 (1997), 113-114. AN INTRODUCTION TO QUANTUM FIELD THEORY by Michael E. Pcstin and Daniel V. Schrocdcr A BOOK REVIEW CHRISTIAN GUNTHER P.O. Box 1465 Libby, MT 59923 USA (Received September 1996; Revised January 1997) Quantum Field Theory arose as an attempt to unify quantum mechanics, classical fields theory, and relativity. These goals have been reached only partially and a rigor- ous foundation of the theory is still missing. However, Quantum Field Theory turned out to be extremely successful in all physical applications: nuclear physics, the theory of matter, elementary particles, high energy physics, and astrophysics. The success of the theory is so overwhelming that even with shaky foundations and many areas still mathematically and conceptionally unresolved there is no doubt that Quantum Field Theory has evolved into a mature subject with a core of established permanent results. Textbooks are good indicators for the state of a theory. Of the many good text- books on Quantum Field Theory, the book under review reflects the maturity of the field: this book manages to represent the core of Quantum Field Theory as a logical and transparent subject. The book is organized in three parts, which cover much of the established material of Quantum Field Theory and standard particle theories. The first part contains the general motivation, fundamental materials, and free quantum fields. A very short section on classical field theory is followed by the quan- tization of the Klein-Gordon field. The authors adopt a purely field-theoretic point of view avoiding the discussion about second quantization. Field quantization is introduced in the usual ad hoc method by writing down the operator valued "equal time" commutation relations. However the concepts of creation/annihilation opera- tots, particles as field excitations with interpretation of position and momentum operators are carefully spelled out and the Lorentz invariance of these concepts is shown. Causality, Propagators and particle creation finish this the treatment of the Klein Gordon field. The Dirac field is discussed with similar diligence paying particu- lar attention to internal symmetries. After introducing free fields, the book turns to the study of renormalizable inter- acting fields: The authors start this study with a short discussion on renormalizabili- ty and then discuss Perturbation, Wicks theorem, S-Matrix, and Feynman rules. The following chapters treat quantum electrodynamics and radiation in detail. This in- Printed in the U.S.A. (1997 by North Atlantic Science Publishing Company 113
Transcript of INTRODUCTION TO QUANTUM FIELDdownloads.hindawi.com/archive/1997/298275.pdf · 2019-08-01 ·...
Journal of Applied Mathematics and Stochastic Analysis, 10:1 (1997), 113-114.
AN INTRODUCTION TO QUANTUM FIELD THEORYby Michael E. Pcstin and Daniel V. Schrocdcr
A BOOK REVIEW
CHRISTIAN GUNTHERP.O. Box 1465
Libby, MT 59923 USA
(Received September 1996; Revised January 1997)
Quantum Field Theory arose as an attempt to unify quantum mechanics, classicalfields theory, and relativity. These goals have been reached only partially and a rigor-ous foundation of the theory is still missing. However, Quantum Field Theory turnedout to be extremely successful in all physical applications: nuclear physics, the theoryof matter, elementary particles, high energy physics, and astrophysics. The success ofthe theory is so overwhelming that even with shaky foundations and many areasstill mathematically and conceptionally unresolved there is no doubt that QuantumField Theory has evolved into a mature subject with a core of established permanentresults.
Textbooks are good indicators for the state of a theory. Of the many good text-books on Quantum Field Theory, the book under review reflects the maturity of thefield: this book manages to represent the core of Quantum Field Theory as a logicaland transparent subject.
The book is organized in three parts, which cover much of the establishedmaterial of Quantum Field Theory and standard particle theories.
The first part contains the general motivation, fundamental materials, and freequantum fields. A very short section on classical field theory is followed by the quan-tization of the Klein-Gordon field. The authors adopt a purely field-theoretic pointof view avoiding the discussion about second quantization. Field quantization isintroduced in the usual ad hoc method by writing down the operator valued "equaltime" commutation relations. However the concepts of creation/annihilation opera-tots, particles as field excitations with interpretation of position and momentumoperators are carefully spelled out and the Lorentz invariance of these concepts isshown. Causality, Propagators and particle creation finish this the treatment of theKlein Gordon field. The Dirac field is discussed with similar diligence paying particu-lar attention to internal symmetries.
After introducing free fields, the book turns to the study of renormalizable inter-acting fields: The authors start this study with a short discussion on renormalizabili-ty and then discuss Perturbation, Wicks theorem, S-Matrix, and Feynman rules. Thefollowing chapters treat quantum electrodynamics and radiation in detail. This in-
Printed in the U.S.A. (1997 by North Atlantic Science Publishing Company 113
114 CHRISTIAN GINTHER
cludes discussions of Compton scattering, infrared divergences, LSZ theory, etc.The middle part of the book is devoted to renormalization. This part begins
with an introduction to functional integration and Maxwell and spinor field quantiza-tion. Chapters on Classification of renormalization and application in 4 and QED,on spontaneous symmetry braking, the renormalization group and Wilson’s approachto renormalization (relationship with statistical mechanics) with applications to phasetransitions and condensed matter systems follow.
The final part of the book covers Non Abelian Gauge Theories and provides thematerials for the standard particle models. A short introductory chapter on gauge in-variance and Yang-Mills fields is followed by the chapters on Quantization of Non-Abelian Gauge Fields, Quantum Chromodynamics, and applications. Gauge fieldswith Spontaneous symmetry braking and weak interactions and, finally, quantizationof spontaneously broken gauge fields follow.
The text is well organized and clearly written. Clarity in (physical) concept andstyle gives the reader the impression to be on firm ground. The book is rich in appli-cations and practical calculations that are explicitly worked out throughout the text.Readers should have background in theoretical mechanics, electrodynamics, andQuantum mechanics, as well as in some elementary tensor analysis and transforma-tion groups.
Problem sections at the end of each chapter provide more insights into the con-
cepts and applications. A major "project" is found after each of the three mainparts.
The covered material is mostly standard and the text uses classical mathematicallanguage. This "conservative" approach could let the subject sometimes appear moresettled than it is. Elementary calculations at times tend to hide the underlyingmathematical structures and here and there intuitive arguments replace rigid proofs.Global topological aspects of gauge theory are not mentioned, and there is no hint tothe problems of the foundations of the theory or to any alternative approaches. Ashort bibliography with comments give hints for more critical studies. There is no
detailed reference section.With this book, the authors have mostly succeeded in their goal to make a diffi-
cult and still unsettled subject accessible to students and non-specialists. It is a valu-able addition to the current literature on this field and it can be warmly recommend-ed as an (even affordable) textbook for a course or for self study.
AN INTRODUCTION TO QUANTUM FIELD THEORYby Michael E. Peskin and Daniel V. SchroederPublisher Addison-WesleyUSA: One Jacob Way, Reading, MA 01867Publication Year 1995ISBN 0-201-50397-2Price: $54.82
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