内容

目次

Preface xi Convention, Notation, and Units xv PART I: MOTIVATIONAND FOUNDATION I.1 Who Needs It? 3 I.2 Path Integral Formulation of QuantumPhysics 7 I.3 From Mattress to Field 16 I.4 From Field to Particle to Force24 I.5 Coulomb and Newton: Repulsion and Attraction 30 I.6 Inverse SquareLaw and the Floating 3-Brane 38 I.7 Feynman Diagrams 41 I.8 QuantizingCanonically and Disturbing the Vacuum.61 I.9 Symmetry 70 I.10 Field Theoryin Curved Spacetime 76 I.11 Field Theory Redux 84 PART II: DIRAC ANDTHE SPINOR II.1 The Dirac Equation 89 II.2 Quantizing the Dirac Field 103II.3 Lorentz Group and Weyl Spinors 111 II.4 Spin-Statistics Connection 117II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions121 II.6 Electron Scattering and Gauge Invariance130 II.7 DiagrammaticProof of Gauge Invariance135 PART III: RENORMALIZATION AND GAUGEINVARIANCE III.1 Cutting Off Our Ignorance 145 III.2 Renormalizable versusNonrenormalizable154 III.3 Counterterms and Physical Perturbation Theory 158III.4 Gauge Invariance: A Photon Can Find No Rest 167 III.5 Field Theorywithout Relativity 172 III.6 The Magnetic Moment of the Electron 177 III.7Polarizing the Vacuum and Renormalizing the Charge.183 PART IV: SYMMETRYAND SYMMETRY BREAKING IV.1 Symmetry Breaking 193 IV.2 The Pion as aNambu-Goldstone Boson 202 IV.3 Effective Potential 208 IV.4 MagneticMonopole 217 IV.5 Nonabelian Gauge Theory 226 IV.6 The Anderson-HiggsMechanism 236 IV.7 Chiral Anomaly 243 PART V: FIELD THEORY ANDCOLLECTIVE PHENOMENA V.1 Superfluids 257 V.2 Euclid, Boltzmann, Hawking,and Field Theory at Finite Temperature 261 V.3 Landau-Ginzburg Theory ofCritical Phenomena 267 V.4 Superconductivity 270 V.5 Peierls Instability273 V.6 Solitons 277 V.7 Vortices, Monopoles, and Instantons 282 PARTVI: FIELD THEORY AND CONDENSED MATTER VI.1 Fractional Statistics,Chern-Simons Term, and Topological Field Theory 293 VI.2 Quantum Hall Fluids300 VI.3 Duality 309 VI.4 The ? Models as Effective Field Theories 318VI.5 Ferromagnets and Antiferromagnets 322 VI.6 Surface Growth and FieldTheory 326 VI.7 Disorder: Replicas and Grassmannian Symmetry 330 VI.8Renormalization Group Flow as a Natural Concept in High Energy and CondensedMatter Physics 337 PART VII: GRAND UNIFICATION VII.1 QuantizingYang-Mills Theory and Lattice Gauge Theory. 353 VII.2 ElectroweakUnification 361 VII.3 Quantum Chromodynamics 368 VII.4 Large N Expansion377 VII.5 Grand Unification 391 VII.6 Protons Are Not Forever 397 VII.7SO(10) Unification 405 PART VIII: GRAVITY AND BEYOND VIII.1 Gravity asa Field Theory and the Kaluza-Klein Picture.419 VIII.2 The CosmologicalConstant Problem and the Cosmic Coincidence Problem 434 VIII.3 EffectiveField Theory Approach to Understanding Nature 437 VIII.4 Supersymmetry: AVery Brief Introduction443 VIII.5 A Glimpse of String Theory as a2-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: VariousIdentities and Feynman Integrals475 E Dotted and Undotted Indices and theMajorana Spinor.479 Solutions to Selected Exercises 483 Further Reading501 Index 505