Quantum Field Theory in a Nutshell 2nd Edition

Table of Contents

• Preface to the Second Edition
• Convention, Notation, and Units
• I 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
  • I.9 Disturbing the Vacuum
  • I.10 Symmetry
  • I.11 Field Theory in Curved Spacetime
  • I.12 Field Theory Redux
• II 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
  • II.8 Photon-Electron Scattering and Crossing
• III 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
  • III.8 Becoming Imaginary and Conserving Probability
• IV 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
• V 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
• VI Part VI: Field Theory and Condensed Matter
  • VI.1 Fractional Statistics, Chern-Simons Term, and Topological Field Theory
  • VI.2 Quantum Hall Fluids
  • VI.3 Duality
  • VI.4 The σ Models as Effective Field Theories
  • VI.5 Ferromagnets and Antiferromagnets
  • VI.6 Surface Growth and Field Theory
  • VI.7 Disorder: Replicas and Grassmannian Symmetry
  • VI.8 Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics
• VII Part VII: Grand Unification
  • VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory
  • VII.2 Electroweak Unification
  • VII.3 Quantum Chromodynamics
  • VII.4 Large N Expansion
  • VII.5 Grand Unification
  • VII.6 Protons Are Not Forever
  • VII.7 SO(10) Unification
• VIII Part VIII: Gravity and Beyond
  • VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture
  • VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problems
  • VIII.3 Effective Field Theory Approach to Understanding Nature
  • VIII.4 Supersymmetry: A Very Brief Introduction
  • VIII.5 A Glimpse of String Theory as a 2-Dimensional Field Theory
  • Closing Words
• N Part N
  • N.1 Gravitational Waves and Effective Field Theory
  • N.2 Gluon Scattering in Pure Yang-Mills Theory
  • N.3 Subterranean Connections in Gauge Theories
  • N.4 Is Einstein Gravity Secretly the Square of Yang-Mills Theory?
  • More Closing Words
• Appendix A: Gaussian Integration and the Central Identity of Quantum Field Theory
• Appendix B: A Brief Review of Group Theory
• Appendix C: Feynman Rules
• Appendix D: Various Identities and Feynman Integrals
• Appendix E: Dotted and Undotted Indices and the Majorana Spinor
• Solutions to Selected Exercises
• Further Reading
• Index