Quantum Field Theory in a Nutshell

An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory - what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments, while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.

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 Invariance 130 II.7 Diagrammatic Proof of Gauge Invariance 135 PART III: RENORMALIZATION AND GAUGE INVARIANCE III.1 Cutting Off Our Ignorance 145 III.2 Renormalizable versus Nonrenormalizable 154 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 s 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 Introduction 443 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 Integrals 475 E. Dotted and Undotted Indices and the Majorana Spinor 479 Solutions to Selected Exercises 483 Further Reading 501 Index 505 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 Integrals 475 E. Dotted and Undotted Indices and the Majorana Spinor 479 Solutions to Selected Exercises 483 Further Reading 501 Index 505