Quantum Field Theory in a Nutshell

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

A. Zee

"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