Part I.Many-Body Systems and Classical Field Theory
1.Classical and Quantum Mechanics of Particle Systems
1.1 Introduction
1.2 Classical Mechanics of Mass Points
1.3 Quantum Mechanics: The Harmonic Oscillator
1.3.1 The Harmonic Oscillator
1.4 The Linear Chain (Classical Treatment)
1.5 The Linear Chain (Quantum Treatment)
2.Classical Field Theory
2.1 Introduction
2.2 The Hamilton Formalism
2.3 Functional Derivatives
2.4 Conservation Laws in Classical Field Theories
2.5 The Generators of the Poincard Group
Part II.Canonical Quantization
3.Nonrelativistic Quantum Field Theory
3.1 Introduction
3.2 Quantization Rules for Bose Particles
3.3 Quantization Rules for Fermi Particles
4.Spin-0 Fields: The Klein-Gordon Equation
4.1 The Neutral Klein-Gordon Field
4.2 The Charged Klein-Gordon Field
4.3 Symmetry Transformations
4.4 The Invariant Commutation Relations
4.5 The Scalar Feynman Propagator
4.6 Supplement: The A Functions
5.Spin-1 Fields: The Dirac Equation
5.1 Introduction
5.2 Canonical Quantization of the Dirac Field
5.3 Plane-Wave Expansion of the Field Operator
5.4 The Feynman Propagator for Dirac Fields
6.Spin-1 Fields: The Maxwell and Proca Equations
6.1 Introduction
6.2 The Maxwell Equations
6.2.1 The Lorentz Gauge
6.2.2 The Coulomb Gauge
6.2.3 Lagrange Density and Conserved Quantities
6.2.4 The Angular-Momentum Tensor
6.3 The Proca Equation
6.4 Plane-Wave Expansion of the Vector Field
6.4.1 The Massive Vector Field
6.4.2 The Massless Vector Field
6.5 Canonical Quantization of the Massive Vector Field
7.Quantization of the Photon Field
7.1 Introduction
7.2 The Electromagnetic Field in Lorentz Gauge
7.3 Canonical Quantization in the Lorentz Gauge
7.3.1 Fourier Decomposition of the Field Operator
7.4 The Gupta-Bleuler Method
7.5 The Feynman Propagator for Photons
7.6 Supplement: Simple Rule for Deriving Feynman Propagators.
7.7 Canonical Quantization in the Coulomb Gauge
7.7.1 The Coulomb Interaction
8.Interacting Quantum Fields
8.1 Introduction
8.2 The Interaction Picture
8.3 The Time-Evolution Operator
8.4 The Scattering Matrix
8.5 Wick's Theorem
8.6 The Feynman Rules of Quantum Electrodynamics
8.7 Appendix: The Scattering Cross Section
9.The Reduction Formalism
9.1 Introduction
9.2 In and Out Fields
9.3 The Lehmann-K~illen Spectral Representation
9.4 The LSZ Reduction Formula
9.5 Perturbation Theory for the n-Point Function
10.Discrete Symmetry Transformations
10.1 Introduction
10.2 Scalar Fields
10.2.1 Space Inversion
10.2.2 Charge Conjugation
10.2.3 Time Reversal
10.3 Dirac Fields
10.3.1 Space Inversion
10.3.2 Charge Conjugation
10.3.3 Time Reversal
10.4 The Electromagnetic Field
10.5 Invariance of the S Matrix
10.6 The CPT Theorem
Part III.Quantization with Path Integrals
11.The Path-Integral Method
11.1 Introduction
11.2 Path Integrals in Nonrelativistic Quantum Mechanics
11.3 Feynman's Path Integral
11.4 The Multi-Dimensional Path Integral
11.5 The Time-Ordered Product and n-Point Functions
11.6 The Vacuum Persistence Amplitude W[J]
12.Path Integrals in Field Theory
12.1 The Path Integral for Scalar Quantum Fields
12.2 Euclidian Field Theory
12.3 The Feynman Propagator
12.4 Generating Functional and Green's Function
12.5 Generating Functional for Interacting Fields
12.6 Green's Functions in Momentum Space
12.7 One-Particle Irreducible Graphs and the Effective Action
12.8 Path Integrals for Fermion Fields
12.9 Generating Functional and Green's Function for Fermion
