The Physics of Quantum Fields

1 Discrete Systems.- 1.1 One-Dimensional Harmonic Crystal.- 1.2 Continuum Limit.- 2 Relativistic Scalar Fields.- 2.1 Conventions.- 2.2 The Klein-Gordon Equation.- 2.3 Symmetries and Noether’s Theorem.- 3 Perturbation Theory.- 3.1 Interactions.- 3.2 Perturbation Theory.- 3.3 Wick’s Theorem.- 4 Feynman Rules.- 4.1 Diagrams.- 4.2 Scattering Theory.- 5 Loops, Unitarity, and Analyticity.- 5.1 Unitarity of the S Matrix.- 5.2 The Analytic S Matrix.- 5.3 Some Loop Diagrams.- 6 Formal Developments.- 6.1 Gell-Mann Low Theorem.- 6.2 Lehmann-Källén Spectral Representation.- 6.3 LSZ Reduction Formulae.- 7 Fermions.- 7.1 Dirac Equation.- 7.2 Spinors, Tensors, and Currents.- 7.3 Holes and the Dirac Sea.- 7.4 Quantization.- 8 QED.- 8.1 Quantizing Maxwell’s Equations.- 8.2 Feynman Rules for QED.- 8.3 Ward Identity and Gauge Invariance.- 9 Electrons in Solids.- 9.1 Second Quantization.- 9.2 Fermi Gas and Fermi Liquid.- 9.3 Electrons and Phonons.- 10 Nonrelativistic Bosons.- 10.1 The Boson Field.- 10.2 Spontaneous Symmetry Breaking.- 10.3 Dilute Bose Gas.- 10.4 Charged Bosons.- 11 Finite Temperature.- 11.1 Partition Functions.- 11.2 Worldlines.- 11.3 Matsubara Sums.- 12 Path Integrals.- 12.1 Quantum Mechanics of a Particle.- 12.2 Gauge Invariance and Operator Ordering.- 12.3 Correlation Functions.- 12.4 Fields.- 12.5 Gaussian Integrals and Free Fields.- 12.6 Perturbation Theory.- 13 Functional Methods.- 13.1 Generating Functionals.- 13.2 Ward Identities.- 14 Path Integrals for Fermions.- 14.1 Berezin Integrals.- 14.2 Fermionic Coherent States.- 14.3 Superconductors.- 15 Lattice Field Theory.- 15.1 Boson Fields.- 15.2 Random Walks.- 15.3 Interactions and Bose Condensation.- 15.4 Lattice Fermions.- 16 The Renormalization Group.- 16.1 Transfer Matrices.- 16.2 Block Spins and Renormalization Group.- 17 Fields and Renormalization.- 17.1 The Free-Field Fixed Point.- 17.2 The Gaussian Model.- 17.3 General Method.- 17.4 Nonlinear ? Model.- 17.5 Renormalizing ??4.- 18 Large N Expansions.- 18.1O(N) Linear ?-Model.- 18.2 Large N Expansions.- A Relativistic State Normalization.- B The General Commutator.- C Dimensional Regularization.- C.1 Analytic Continuation and Integrals.- C.2 Propagators.- D Spinors and the Principle of the Sextant.- D.1 Constructing the ?-Matrices.- D.2 Basic Theorem.- D.3 Chirality.- E Indefinite Metric.- F Phonons and Momentum.- G Determinants in Quantum Mechanics.