Undergraduate Lecture Notes in Physics

Series Editors

Neil Ashby, University of Colorado, Boulder, CO, USA

William Brantley, Department of Physics, Furman University, Greenville, SC, USA

Matthew Deady, Physics Program, Bard College, Annandale-on-Hudson, NY, USA

Michael Fowler, Department of Physics, University of Virginia, Charlottesville,VA, USA

Morten Hjorth-Jensen, Department of Physics, University of Oslo, Oslo, Norway

Michael Inglis, Department of Physical Sciences, SUNY Suffolk CountyCommunity College, Selden, NY, USA

Undergraduate Lecture Notes in Physics (ULNP) publishes authoritative textscovering topics throughout pure and applied physics. Each title in the series issuitable as a basis for undergraduate instruction, typically containing practiceproblems, worked examples, chapter summaries, and suggestions for further reading.

ULNP titles must provide at least one of the following:

• An exceptionally clear and concise treatment of a standard undergraduatesubject.

• A solid undergraduate-level introduction to a graduate, advanced, ornon-standard subject.

• A novel perspective or an unusual approach to teaching a subject.

ULNP especially encourages new, original, and idiosyncratic approaches to physicsteaching at the undergraduate level.

The purpose of ULNP is to provide intriguing, absorbing books that will continue tobe the reader’s preferred reference throughout their academic career.

More information about this series at http://www.springer.com/series/8917

Masud Chaichian • Hugo Perez Rojas •

Anca Tureanu

Basic Concepts in PhysicsFrom the Cosmos to Quarks

Second Edition

123

Masud ChaichianDepartment of PhysicsUniversity of HelsinkiHelsinki, Finland

Anca TureanuDepartment of PhysicsUniversity of HelsinkiHelsinki, Finland

Hugo Perez RojasDepartment of Theoretical PhysicsICIMAFLa Habana, Cuba

ISSN 2192-4791 ISSN 2192-4805 (electronic)Undergraduate Lecture Notes in PhysicsISBN 978-3-662-62312-1 ISBN 978-3-662-62313-8 (eBook)https://doi.org/10.1007/978-3-662-62313-8

1st edition: © Springer-Verlag Berlin Heidelberg 20142nd edition: © Springer-Verlag GmbH Germany, part of Springer Nature 2021This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part ofSpringer Nature.The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

Preface to the Second Edition

The praise of the first edition of the book by many readers encouraged us to preparethe present second edition. We express our deep gratitude to all those readers fortheir remarks and suggestions – in this edition we have tried to take into account allof them as much as possible, and as well to come up with their wishes to includesome problems to be solved, together with their solutions or at least sufficient hintsto solve them.

As its previous edition, this book is intended for undergraduate students, physicsteachers, students in high schools, researchers and general readers interested toknow what physics is about together with its latest developments and discoveries.

Thinking about the book to be useful also as a textbook, totally or in part, wehave added several new topics with the latest findings in those fields. For instance,the recent discovery of gravitational waves, as one of the most importantachievements of modern physical sciences, is presented in Chap. 10. At the end ofChaps. 1–11 some problems are included with their solutions or hints how to solvethem given at the end of the book. Those problems are useful for a complementaryunderstanding of the theories and their implication. However, for non-specializedreaders it is recommended to bypass, at least in their first-time reading, the problemsas well as the mathematical details.

The added new topics also provide connections among the subjects treated indifferent chapters. For instance, the wobble of some stars interacting with theirplanets, as explained by the two body Kepler problem, helps to detect invisiblecompanions, by using Doppler spectroscopy of the star light. The Clapeyron–Clausius equation helps to understand the development of life at dark, deep and hotoceanic vents at high pressures, as well as why the hot Earth nucleus is solid. Thecreation of the magnetosphere is explained as due to the deviation of the solar windby the Earth magnetic field. A reference to the former experiments is made in orderto resolve the loophole appeared there and to support, thanks to more recentexperiments, the occurrence of quantum entanglement, and to show the validityof the violation of Bell inequalities as a genuine quantum phenomenon.Gravitational lensing, as well as the correction of time for GPS satellites, as the

v

technical applications of special and general relativity, are explained. Some earlierfigures have been improved and new ones were added.

Our special thanks go to François Englert, Igal Galili, and Markku Oksanen fortheir valuable comments and advice.

Helsinki, Finland Masud ChaichianLa Habana, Cuba Hugo Perez RojasHelsinki, Finland Anca TureanuMay 2021

vi Preface to the Second Edition

Preface to the First Edition

This book is the outcome of many lectures, seminars, and colloquia the authorshave given on different occasions to different audiences in several countries over along period of time and the experience and feedback obtained from them. With awide range of readers in mind, some topics have been presented in twofold form,both descriptively and more formally.

This book is intended not only for first to second year undergraduate students, asa complement to specialized textbooks but also for physics teachers and students inhigh schools. At the same time, it is addressed to researchers and scientists in otherfields, including engineers and general readers interested in acquiring an overviewof modern physics. A minimal mathematical background, up to elementary cal-culus, matrix algebra and vector analysis, is required. However, mathematicaltechnicalities have not been stressed, and long calculations have been avoided. Thebasic and most important ideas have been presented with a view to introducing thephysical concepts in a pedagogical way. Since some specific topics of modernphysics, particularly those related to quantum theory, are an important ingredient ofstudent courses nowadays, the first five chapters on classical physics are presentedkeeping in mind their connection to modern physics whenever possible.

In most chapters, historical facts are included. Several themes are discussedwhich are sometimes omitted in basic courses on physics. For instance, the relationbetween entropy and information, exchange energy and ferromagnetism, super-conductivity and the relation between phase transitions and spontaneous symmetrybreaking, chirality, the fundamental C, P, and T invariances, paradoxes of quantumtheory, the problem of measurement in quantum mechanics, quantum statistics andspecific heat in solids, quantum Hall effect, graphene, general relativity and cos-mology, CP violation, Casimir and Aharonov–Bohm effects, causality, unitarity,spontaneous symmetry breaking and the Standard Model, inflation, baryogenesis,and nucleosynthesis, ending with a chapter on the relationship between physics andlife, including biological chiral symmetry breaking.

To non-specialized readers it is recommended to bypass, at least on a firstreading, the mathematical content of sections and subsections 1.8, 1.9, 2.5, 3.11,4.5, 6.7, 6.8.1, 7.3, 7.4.1, 8.2, 10.3, and 10.5.

vii

During the preparation of this book the authors have benefited greatly fromdiscussions with many of their colleagues and students, to whom we are indebted. Itis a pleasure to express our gratitude in particular to Cristian Armendariz-Picon,Alexander D. Dolgov, François Englert, Josef Kluson, Vladimir M. Mostepanenko,Viatcheslav Mukhanov, Markku Oksanen, Roberto Sussmann, and Ruibin Zhangfor their stimulating suggestions and comments, while our special thanks go toTiberiu Harko, Peter Prešnajder and Daniel Radu, to whom we are most grateful fortheir valuable advice in improving an initial version of the manuscript.

Helsinki, Finland Masud ChaichianLa Habana, Cuba Hugo Perez RojasHelsinki, Finland Anca TureanuMarch 2013

viii Preface to the First Edition

Contents

1 Gravitation and Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 From Pythagoras to the Middle Ages . . . . . . . . . . . . . . . . . . . 21.2 Copernicus, Kepler, and Galileo . . . . . . . . . . . . . . . . . . . . . . . 61.3 Newton and Modern Science . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4.1 Newton’s First Law . . . . . . . . . . . . . . . . . . . . . . . . 151.4.2 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . 151.4.3 Planetary Motion in Newton’s Theory . . . . . . . . . . . 241.4.4 Newton’s Third Law . . . . . . . . . . . . . . . . . . . . . . . . 26

1.5 Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.5.1 Conservation of Linear Momentum . . . . . . . . . . . . . 281.5.2 Conservation of Angular Momentum . . . . . . . . . . . . 291.5.3 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . 30

1.6 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351.7 Inertial and Non-inertial Systems . . . . . . . . . . . . . . . . . . . . . . 361.8 Rigid Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401.9 The Principle of Least Action . . . . . . . . . . . . . . . . . . . . . . . . 421.10 Hamilton Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461.11 Complements on Gravity and Planetary Motion . . . . . . . . . . . 481.12 Advice for Solving Problems . . . . . . . . . . . . . . . . . . . . . . . . . 57Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

2 Entropy, Statistical Physics, and Information . . . . . . . . . . . . . . . . . 632.1 Thermodynamic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.1.1 First Law of Thermodynamics . . . . . . . . . . . . . . . . . 652.1.2 Second Law of Thermodynamics . . . . . . . . . . . . . . . 662.1.3 Third Law of Thermodynamics . . . . . . . . . . . . . . . . 672.1.4 Thermodynamic Potentials . . . . . . . . . . . . . . . . . . . 67

ix

2.2 Statistical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.3 Entropy and Statistical Physics . . . . . . . . . . . . . . . . . . . . . . . 742.4 Temperature and Chemical Potential . . . . . . . . . . . . . . . . . . . 762.5 Statistical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.5.1 Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . 792.5.2 Maxwell Distribution . . . . . . . . . . . . . . . . . . . . . . . 852.5.3 Grand Canonical Ensemble . . . . . . . . . . . . . . . . . . . 86

2.6 Entropy and Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872.7 Maxwell’s Demon and Perpetuum Mobile . . . . . . . . . . . . . . . 892.8 First Order Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 96Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3 Electromagnetism and Maxwell’s Equations . . . . . . . . . . . . . . . . . . 1013.1 Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.2 Electrostatic and Gravitational Fields . . . . . . . . . . . . . . . . . . . 1063.3 Conductors, Semiconductors, and Insulators . . . . . . . . . . . . . . 1073.4 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083.5 Magnetic Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1103.6 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.6.1 Gauss’s Law for Electric Fields . . . . . . . . . . . . . . . . 1113.6.2 Gauss’s Law for Magnetism . . . . . . . . . . . . . . . . . . 1123.6.3 Faraday’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1143.6.4 Ampère–Maxwell Law . . . . . . . . . . . . . . . . . . . . . . 115

3.7 Lorentz Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1163.8 Fields in a Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1203.9 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3.9.1 Diamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.9.2 Paramagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1243.9.3 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 1253.9.4 Ferrimagnetism, Antiferromagnetism, and

Magnetic Frustration . . . . . . . . . . . . . . . . . . . . . . . . 1263.9.5 Spin Ices and Monopoles . . . . . . . . . . . . . . . . . . . . 127

3.10 Second Order Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . 1283.11 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . 1283.12 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1303.13 Meissner Effect: Type I and II Superconductors . . . . . . . . . . . 1313.14 Appendix of Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

x Contents

4 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1374.1 Waves in a Medium and in Æther . . . . . . . . . . . . . . . . . . . . . 1384.2 Electromagnetic Waves and Maxwell’s Equations . . . . . . . . . . 139

4.2.1 Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . 1414.2.2 Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

4.3 Generation of Electromagnetic Waves . . . . . . . . . . . . . . . . . . 1434.3.1 Retarded Potentials . . . . . . . . . . . . . . . . . . . . . . . . . 1434.3.2 Mechanisms Generating Electromagnetic Waves . . . . 144

4.4 Wave Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.4.1 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1454.4.2 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1484.4.3 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1524.4.4 Spectral Composition . . . . . . . . . . . . . . . . . . . . . . . 154

4.5 Fourier Series and Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 1574.6 Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1594.7 Dispersion of Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1614.8 Black Body Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

5 Special Theory of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1675.1 Postulates of Special Relativity . . . . . . . . . . . . . . . . . . . . . . . 1685.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1715.3 Light Cone and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . 1765.4 Contraction of Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1775.5 Time Dilation: Proper Time . . . . . . . . . . . . . . . . . . . . . . . . . . 1785.6 Addition of Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1815.7 Relativistic Four-Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1825.8 Electrodynamics in Relativistically Covariant Formalism . . . . . 1845.9 Energy and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1865.10 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1885.11 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1895.12 Tachyons and Superluminal Signals . . . . . . . . . . . . . . . . . . . . 1905.13 The Lagrangian for a Particle in an Electromagnetic Field . . . . 192Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

6 Atoms and Quantum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1976.1 Motion of a Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1976.2 Evolution of the Concept of Atom . . . . . . . . . . . . . . . . . . . . . 2006.3 Rutherford’s Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006.4 Bohr’s Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2016.5 Schrödinger’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2046.6 Wave Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Contents xi

6.7 Operators and States in Quantum Mechanics . . . . . . . . . . . . . 2146.8 One-Dimensional Systems in Quantum Mechanics . . . . . . . . . 219

6.8.1 The Infinite Potential Well . . . . . . . . . . . . . . . . . . . 2196.8.2 Quantum Harmonic Oscillator . . . . . . . . . . . . . . . . . 2206.8.3 Charged Particle in a Constant Magnetic Field . . . . . 224

6.9 Emission and Absorption of Radiation . . . . . . . . . . . . . . . . . . 2256.10 Stimulated Emission and Lasers . . . . . . . . . . . . . . . . . . . . . . . 2266.11 Tunnel Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2286.12 Indistinguishability and Pauli’s Principle . . . . . . . . . . . . . . . . 2296.13 Exchange Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2306.14 Exchange Energy and Ferromagnetism . . . . . . . . . . . . . . . . . . 2316.15 Distribution of Electrons in the Atom . . . . . . . . . . . . . . . . . . . 2316.16 Quantum Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

6.16.1 U and R Evolution Procedures . . . . . . . . . . . . . . . . 2346.16.2 On Theory and Observable Quantities . . . . . . . . . . . 235

6.17 Paradoxes in Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . 2366.17.1 De Broglie’s Paradox . . . . . . . . . . . . . . . . . . . . . . . 2366.17.2 Schrödinger’s Cat Paradox . . . . . . . . . . . . . . . . . . . 2376.17.3 Toward the EPR Paradox . . . . . . . . . . . . . . . . . . . . 2386.17.4 A Hidden Variable Model and Bell’s Theorem . . . . . 2406.17.5 Bell Inequality and Conventional Quantum

Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2426.17.6 EPR Paradox: Quantum Mechanics Versus Special

Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2426.18 Quantum Computation and Teleportation . . . . . . . . . . . . . . . . 2446.19 Classical vs. Quantum Logic . . . . . . . . . . . . . . . . . . . . . . . . . 245Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

7 Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2497.1 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

7.1.1 The Spin of the Electron . . . . . . . . . . . . . . . . . . . . . 2497.1.2 Hydrogen Atom in Dirac’s Theory . . . . . . . . . . . . . 2557.1.3 Hole Theory and Positrons . . . . . . . . . . . . . . . . . . . 256

7.2 Intermezzo: Natural Units and the Metric Used in ParticlePhysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

7.3 Quantized Fields and Particles . . . . . . . . . . . . . . . . . . . . . . . . 2607.4 Quantum Electrodynamics (QED) . . . . . . . . . . . . . . . . . . . . . 264

7.4.1 Unitarity in Quantum Electrodynamics . . . . . . . . . . . 2657.4.2 Feynman Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 2677.4.3 Virtual Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 2687.4.4 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . 2707.4.5 Electron Self-energy and Vacuum Polarization . . . . . 2727.4.6 Renormalization and Running Coupling Constant . . . 275

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7.5 Quantum Vacuum and Casimir Effect . . . . . . . . . . . . . . . . . . . 2777.6 Principle of Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . 2797.7 CPT Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2837.8 Grassmann Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

8 Fermi–Dirac and Bose–Einstein Statistics . . . . . . . . . . . . . . . . . . . . 2898.1 Fermi–Dirac Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2898.2 Fermi–Dirac and Bose–Einstein Distributions . . . . . . . . . . . . . 2918.3 The Ideal Electron Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2938.4 Heat Capacity of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2958.5 Metals, Semiconductors, and Insulators . . . . . . . . . . . . . . . . . 2988.6 Electrons and Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2998.7 Applications of the Fermi–Dirac Statistics . . . . . . . . . . . . . . . 299

8.7.1 Quantum Hall Effect . . . . . . . . . . . . . . . . . . . . . . . . 2998.7.2 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

8.8 Bose–Einstein Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3088.9 Einstein–Debye Theory of Heat Capacity . . . . . . . . . . . . . . . . 3098.10 Bose–Einstein Condensation . . . . . . . . . . . . . . . . . . . . . . . . . 3128.11 Quantum Coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3158.12 Nonrelativistic Quantum Gases . . . . . . . . . . . . . . . . . . . . . . . 316Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

9 Four Fundamental Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3219.1 Gravity and Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . 3219.2 Atomic Nuclei and Nuclear Phenomena . . . . . . . . . . . . . . . . . 3229.3 Strong Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3249.4 Weak Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3269.5 Parity Non-Conservation in Beta Decay . . . . . . . . . . . . . . . . . 3279.6 Violation of CP and T Invariance . . . . . . . . . . . . . . . . . . . . . 3299.7 Some Significant Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 3319.8 Death of Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3339.9 Neutron Stars and Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . 335Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

10 General Relativity and Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . 33910.1 Principle of Equivalence and General Relativity . . . . . . . . . . . 34010.2 Gravitational Field and Geometry . . . . . . . . . . . . . . . . . . . . . . 34210.3 Affine Connection and Metric Tensor . . . . . . . . . . . . . . . . . . . 34910.4 Gravitational Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . 35110.5 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

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10.6 Gravitational Radius and Collapse . . . . . . . . . . . . . . . . . . . . . 35810.6.1 Wormholes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36210.6.2 Dark Matter, Dark Energy, and Accelerated

Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36310.7 Gravitation and Quantum Effects . . . . . . . . . . . . . . . . . . . . . . 36410.8 Cosmic Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

11 Unification of the Forces of Nature . . . . . . . . . . . . . . . . . . . . . . . . . 36911.1 Theory of Weak Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 36911.2 Yang–Mills Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37311.3 Nambu–Goldstone Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 37611.4 Brout–Englert–Higgs Mechanism . . . . . . . . . . . . . . . . . . . . . . 37811.5 Glashow–Salam–Weinberg Model . . . . . . . . . . . . . . . . . . . . . 37911.6 Electroweak Phase Transition . . . . . . . . . . . . . . . . . . . . . . . . . 38411.7 Hadrons and Quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38511.8 Neutrino Oscillations and Masses . . . . . . . . . . . . . . . . . . . . . . 39011.9 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 39311.10 Grand Unification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39611.11 Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39811.12 Supersymmetry and Superstrings . . . . . . . . . . . . . . . . . . . . . . 399Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

12 Physics and Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40512.1 Order and Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40512.2 Life and Fundamental Interactions . . . . . . . . . . . . . . . . . . . . . 40912.3 Homochirality: Biological Symmetry Breaking . . . . . . . . . . . . 40912.4 Neutrinos and Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 41112.5 Anthropic Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41312.6 Search for Extraterrestrial Life . . . . . . . . . . . . . . . . . . . . . . . . 414Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

Appendix: Solutions of the Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

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