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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