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Quantum Field Theory in a Nutshell


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A beautiful exposition of the way modern field theorists think about quantum field theory, packed with insights and physical intuition. Zee's book should be required reading for every serious student of the subject. -- Nima Arkani-Hamed, Institute for Advanced Study

Table of Contents

Preface xi Convention, Notation, and Units xv PART I: MOTIVATION AND FOUNDATION I.1 Who Needs It? 3 I.2 Path Integral Formulation of Quantum Physics 7 I.3 From Mattress to Field 16 I.4 From Field to Particle to Force 24 I.5 Coulomb and Newton: Repulsion and Attraction 30 I.6 Inverse Square Law and the Floating 3-Brane 38 I.7 Feynman Diagrams 41 I.8 Quantizing Canonically and Disturbing the Vacuum.61 I.9 Symmetry 70 I.10 Field Theory in Curved Spacetime 76 I.11 Field Theory Redux 84 PART II: DIRAC AND THE SPINOR II.1 The Dirac Equation 89 II.2 Quantizing the Dirac Field 103 II.3 Lorentz Group and Weyl Spinors 111 II.4 Spin-Statistics Connection 117 II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions 121 II.6 Electron Scattering and Gauge Invariance130 II.7 Diagrammatic Proof of Gauge Invariance135 PART III: RENORMALIZATION AND GAUGE INVARIANCE III.1 Cutting Off Our Ignorance 145 III.2 Renormalizable versus Nonrenormalizable154 III.3 Counterterms and Physical Perturbation Theory 158 III.4 Gauge Invariance: A Photon Can Find No Rest 167 III.5 Field Theory without Relativity 172 III.6 The Magnetic Moment of the Electron 177 III.7 Polarizing the Vacuum and Renormalizing the Charge.183 PART IV: SYMMETRY AND SYMMETRY BREAKING IV.1 Symmetry Breaking 193 IV.2 The Pion as a Nambu-Goldstone Boson 202 IV.3 Effective Potential 208 IV.4 Magnetic Monopole 217 IV.5 Nonabelian Gauge Theory 226 IV.6 The Anderson-Higgs Mechanism 236 IV.7 Chiral Anomaly 243 PART V: FIELD THEORY AND COLLECTIVE PHENOMENA V.1 Superfluids 257 V.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature 261 V.3 Landau-Ginzburg Theory of Critical Phenomena 267 V.4 Superconductivity 270 V.5 Peierls Instability 273 V.6 Solitons 277 V.7 Vortices, Monopoles, and Instantons 282 PART VI: FIELD THEORY AND CONDENSED MATTER VI.1 Fractional Statistics, Chern-Simons Term, and Topological Field Theory 293 VI.2 Quantum Hall Fluids 300 VI.3 Duality 309 VI.4 The ? Models as Effective Field Theories 318 VI.5 Ferromagnets and Antiferromagnets 322 VI.6 Surface Growth and Field Theory 326 VI.7 Disorder: Replicas and Grassmannian Symmetry 330 VI.8 Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics 337 PART VII: GRAND UNIFICATION VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory. 353 VII.2 Electroweak Unification 361 VII.3 Quantum Chromodynamics 368 VII.4 Large N Expansion 377 VII.5 Grand Unification 391 VII.6 Protons Are Not Forever 397 VII.7 SO(10) Unification 405 PART VIII: GRAVITY AND BEYOND VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture.419 VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problem 434 VIII.3 Effective Field Theory Approach to Understanding Nature 437 VIII.4 Supersymmetry: A Very Brief Introduction443 VIII.5 A Glimpse of String Theory as a 2-Dimensional Field Theory 452 Closing Words 455 APPENDIXES: A: Gaussian Integration and the Central Identity of Quantum Field Theory 459 B: A Brief Review of Group Theory 461 C: Feynman Rules 471 D: Various Identities and Feynman Integrals475 E Dotted and Undotted Indices and the Majorana Spinor.479 Solutions to Selected Exercises 483 Further Reading 501 Index 505

About the Author

A. Zee is professor of physics and a permanent member of the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. His books include "Fearful Symmetry: The Search for Beauty in Modern Physics" (Princeton).


"Every theoretical physicist and every university library should own this book."--Choice "This is quantum field theory taught at the knee of ... one who loves the grandeur of his subject, has a keen eye for a slick argument, and is eager to share his repertoire of anecdotes about Feynman, Fermi, and all of his heroes... Zee misses no opportunity to point out that an argument he gives opens the door to some deeper subject that he encourages the reader to explore... [Quantum Field Theory in a Nutshell] helps them love the subject and race to its frontier."--Michael E. Peskin, Classical and Quantum Gravity "[T]his is an excellent and unique introduction to quantum field theory. It takes a lot of work, and capable but less confident students would need a great deal of guidance, but it is a beautiful text written with infectious enthusiasm, and I thoroughly recommend it."--S. Virmani, Contemporary Physics "[This] is an excellent invitation to the wide area of modern quantum field theory, and even provides the mature field theoretician with interesting insights and connections. To the curious student, it is a near-perfect companion to spice up the world of quantum field theory, especially particle physics, beyond the standard presentations... It is definitely highly recommendable to anyone who wants to have a book with a non-standard view on quantum field theory, or who just wants to have an entertaining and insightful reprise of the topic."--Axel Maas, Mathematical Reviews Clippings

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