| This book differs from other quantum field theory books that have come out inrecent years in several respects. |
| Preface Convention， Notation， and Units PART Ⅰ MOTIVATION AND FOUNDATION Ⅰ.1 Who Needs It? Ⅰ.2 Path Integral Formulation of Quantum Physics Ⅰ.3 From Mattress to Field Ⅰ.4 From Field to Particle to Force Ⅰ.5 Coulomb and Newton： Repulsion and Attraction Ⅰ.6 Inverse Square Law and the Floating 3-Brane Ⅰ.7 Feynman Diagrams Ⅰ.8 Quantizing Canonically and Disturbing the Vacuum Ⅰ.9 Symmetry Ⅰ.10 Field Theory in Curved Spacetime Ⅰ.11 Field Theory Redux PART Ⅱ DIRAC AND THE SPINOR Ⅱ.1 The Dirac Equation Ⅱ.2 Quantizing the Dirac Field Ⅱ.3 Lorentz Group and Weyl Spinors Ⅱ.4 Spin-Statistics Connection Ⅱ.5 Vacuum Energy， Grassmann Integrals， and Feynman Diagrams for Fermions Ⅱ.6 Electron Scattering and Gauge Invariance Ⅱ.7 Diagrammatic Proof of Gauge Invariance PART Ⅲ RENORMALIZATION AND GAUGE INVARIANCE Ⅲ.1 Cutting Off Our Ignorance Ⅲ.2 Renormalizable versus Nonrenormalizable Ⅲ.3 Counterterms and Physical Perturbation Theory Ⅲ.4 Gauge Invariance： A Photon Can Find No Rest Ⅲ.5 Field Theory without Relativity Ⅲ.6 The Magnetic Moment of the Electron Ⅲ.7 Polarizing the Vacuum and Renormalizing the Charge PART Ⅳ SYMMETRY AND SYMMETRY BREAKING Ⅳ.1 Symmetry Breaking Ⅳ.2 The Pion as a Nambu-Goldstone Boson Ⅳ.3 Effective Potential Ⅳ.4 Magnetic Monopole Ⅳ.5 Nonabelian Gauge Theory Ⅳ.6 The Anderson-Higgs Mechanism Ⅳ.7 Chiral Anomaly PART Ⅴ FIELD THEORY AND COLLECTIVE PHENOMENA Ⅴ.1 Superfluids Ⅴ.2 Euclid， Boltzmann， Hawking， and Field Theory at Finite Temperature Ⅴ.3 Landau-Ginzburg Theory of Critical Phenomena Ⅴ.4 Superconductivity Ⅴ.5 Peierls Instability Ⅴ.6 Solitons Ⅴ.7 Vortices， Monopoles， and Instantons PART Ⅵ FIELD THEORY AND CONDENSED MATTER Fractional Statistics， Chem-Simons Term， and Topological Field Theory Quantum Hall Fluids Duality The δ Models as Effective Field Theories Ferromagnets and Antiferromagnets Surface Growth and Field Theory Disorder： Replicas and Grassmannian Symmetry Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics PART Ⅶ GRAND UNIFICATION Quantizing Yang-Mills Theory and Lattice Gauge Theory . Electroweak Unification Quantum Chromodynamics Large N Expansion Grand Unification Protons Are Not Forever SO(10) Unification PART Ⅷ GRAVITY AND BEYOND Gravity as a Field Theory and the Kaluza-Klein Picture The Cosmological Constant Problem and the Cosmic Coincidence Problem Effective Field Theory Approach to Understanding Nature . Supersymmetry： A Very Brief Introduction A Glimpse of String Theory as a 2-Dimensional Field Theory Closing Words APPENDIXES A Gaussian Integration and the Central Identity of Quantum Field Theory B A Brief Review of Group Theory C Feynman Rules D Various Identities and Feynman Integrals E Dotted and Undotted Indices and the Majorana Spinor Solutions to Selected Exercises Further Reading Index |
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