The Physics of Quantum Fields

by Michael Stone

1 Discrete Systems.- 1.1 One-Dimensional Harmonic Crystal.- 1.1.1 Normal Modes.- 1.1.2 Harmonic Oscillator.- 1.1.3 Annihilation and Creation Operators for Normal Modes.- 1.2 Continuum Limit.- 1.2.1 Sums and Integrals.- 1.2.2 Continuum Fields.- 2 Relativistic Scalar Fields.- 2.1 Conventions.- 2.2 The Klein-Gordon Equation.- 2.2.1 Relativistic Normalization.- 2.2.2 An Inner Product.- 2.2.3 Complex Scalar Fields.- 2.3 Symmetries and Noether's Theorem.- 2.3.1 Internal Symmetries.- 2.3.2 Space-Time Symmetries.- 3 Perturbation Theory.- 3.1 Interactions.- 3.2 Perturbation Theory.- 3.2.1 Interaction Picture.- 3.2.2 Propagators and Time-Ordered Products.- 3.3 Wick's Theorem.- 3.3.1 Normal Products.- 3.3.2 Wick's Theorem.- 3.3.3 Applications.- 4 Feynman Rules.- 4.1 Diagrams.- 4.1.1 Diagrams in Space-time.- 4.1.2 Diagrams in Momentum Space.- 4.2 Scattering Theory.- 4.2.1 Cross-Sections.- 4.2.2 Decay of an Unstable Particle.- 5 Loops, Unitarity, and Analyticity.- 5.1 Unitarity of the S Matrix.- 5.2 The Analytic S Matrix.- 5.2.1 Origin of Analyticity.- 5.2.2 Unitarity and Branch Cuts.- 5.2.3 Resonances, Widths, and Lifetimes.- 5.3 Some Loop Diagrams.- 5.3.1 Wick Rotation.- 5.3.2 Feynman Parameters.- 5.3.3 Dimensional Regularization.- 6 Formal Developments.- 6.1 Gell-Mann Low Theorem.- 6.2 Lehmann-Källén Spectral Representation.- 6.3 LSZ Reduction Formulae.- 6.3.1 Amputation of External Legs.- 6.3.2 In and Out States and Fields.- 6.3.3 Borcher's Classes.- 7 Fermions.- 7.1 Dirac Equation.- 7.2 Spinors, Tensors, and Currents.- 7.2.1 Field Bilinears.- 7.2.2 Conservation Laws.- 7.3 Holes and the Dirac Sea.- 7.3.1 Positive and Negative Energies.- 7.3.2 Holes.- 7.4 Quantization.- 7.4.1 Normal and Time-Ordered Products.- 8 QED.- 8.1 Quantizing Maxwell's Equations.- 8.1.1 Hamiltonian Formalism.- 8.1.2 Axial Gauge.- 8.1.3 Lorentz Gauge.- 8.2 Feynman Rules for QED.- 8.2.1 Moller Scattering.- 8.3 Ward Identity and Gauge Invariance.- 8.3.1 The Ward Identity.- 8.3.2 Applications.- 9 Electrons in Solids.- 9.1 Second Quantization.- 9.2 Fermi Gas and Fermi Liquid.- 9.2.1 One-Particle Density Matrix.- 9.2.2 Linear Response.- 9.2.3 Diagram Approacha.- 9.2.4 Applications.- 9.3 Electrons and Phonons.- 10 Nonrelativistic Bosons.- 10.1 The Boson Field.- 10.2 Spontaneous Symmetry Breaking.- 10.3 Dilute Bose Gas.- 10.3.1 Bogoliubov Transfomation.- 10.3.2 Field Equations.- 10.3.3 Quantization.- 10.3.4 Landau Criterion for Superfluidity.- 10.3.5 Normal and Superfluid Densities.- 10.4 Charged Bosons.- 10.4.1 Gross-Pitaevskii Equation.- 10.4.2 Vortices.- 10.4.3 Connection with Fluid Mechanics.- 11 Finite Temperature.- 11.1 Partition Functions.- 11.2 Worldlines.- 11.3 Matsubara Sums.- 12 Path Integrals.- 12.1 Quantum Mechanics of a Particle.- 12.1.1 Real Time.- 12.1.2 Euclidean Time.- 12.2 Gauge Invariance and Operator Ordering.- 12.3 Correlation Functions.- 12.4 Fields.- 12.5 Gaussian Integrals and Free Fields.- 12.5.1 Real Fields.- 12.5.2 Complex Fields.- 12.6 Perturbation Theory.- 13 Functional Methods.- 13.1 Generating Functionals.- 13.1.1 Effective Action.- 13.2 Ward Identities.- 13.2.1 Goldstone's Theorem.- 14 Path Integrals for Fermions.- 14.1 Berezin Integrals.- 14.1.1 A Simple Supersymmetry.- 14.2 Fermionic Coherent States.- 14.3 Superconductors.- 14.3.1 Effective Action.- 15 Lattice Field Theory.- 15.1 Boson Fields.- 15.2 Random Walks.- 15.3 Interactions and Bose Condensation.- 15.3.1 Rotational Invariance.- 15.4 Lattice Fermions.- 15.4.1 No Chiral Lattice Fermions.- 16 The Renormalization Group.- 16.1 Transfer Matrices.- 16.1.1 Continuum Limit.- 16.1.2 Two-Dimensional Ising Model.- 16.2 Block Spins and Renormalization Group.- 16.2.1 Correlation Functions.- 17 Fields and Renormalization.- 17.1 The Free-Field Fixed Point.- 17.2 The Gaussian Model.- 17.3 General Method.- 17.4 Nonlinear ? Model.- 17.4.1 Renormalizing.- 17.4.2 Solution of the RGE.- 17.5 Renormalizing ??4.- 18 Large N Expansions.- 18.1 O(N) Linear ?-Model.- 18.2 Large N Expansions.- 18.2.1

288 pages, Paperback

First published December 28, 1999

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Reviews

[To Chin · Rating 3 out of 5]

Nice bird's-eye view of QFT.