量子场物理学

前言

　　This book is intended to provide a general introduction to the physics of quantized fields and many-body physics. It is based on a two-semester sequence of courses taught at the University of Illinois at Urbana-Champaign at various times between 1985 and 1997. The students taking all or part of the sequence had interests ranging from particle and nuclear theory through quantum optics to condensed matter physics experiment.　　The book does not cover as much ground as some texts. This is because I have tried to concentrate on the basic conceptual issues that many students find difficult. For a computation-method oriented course an instructor would probably wish to suplement this book with a more comprehensive and specialized text such as Peskin and Schroeder An Introduction to Quantum Field Theory， which is intended for particle theorists， or perhaps the venerable Quantum Theory of Many-Particle Systems by Fetter and Walecka.　　The most natural distribution of the material if the book is used for a two-semster course is as follows：　　1st Semester：. Chapters 1-11.　　2nd semester： Chapters 12-18.　　The material in the first 11 chapters is covered using traditional quantum me- chanics operator language. This is because the text is intended for people with a wide range of interests. Were I writing for particle-theory students only， I would start with path integrals from chapter one. For a broader readership， it seems useful to maintain continuity with traditional hamiltonian quantum mechanics for as long as one as there is no penalty in ease of comprehension —— and this is the case with the simple field theories discussed in the earlier chapters.

书籍目录

Preface1 Discrete Systems1.1 One-Dimensional Harmonic Crystal1.1.1 Normal Modes1.1.2 Harmonic Oscillator1.1.3 Annihilation and Creation Operators for Normal Modes1.2 Continuum Limit1.2.1 Sums and Integrals1.2.2 Continuum Fields2 Relativistic Scalar Fields2.1 Convcntions2.2 The Klein-Gordon Equation2.2.1 Relativistic Normalization2.2.2 An Inner Product2.2.3 Complex Scalar Fields2.3 Symmetries and Noethers Theorem2.3.1 Internal Symmetries2.3.2 Space-Time Symmetries3 Perturbation Theory3.1 Interactions3.2 Perturbation Theory3.2.1 Interaction Picture3.2.2 Propagators and Time-Ordered Products3.3 Wicks Theorem3.3.1 Normal Products3.3.2 Wicks Theorem3.3.3 Applications4 Feynman Rules4.1 Diagrams4.1.1 Diagrams in Space-time4.1.2 Diagrams in Momentum Space4.2 Scattering Theory4.2.1 Cross-Sections4.2.2 Decay of an Unstable Particle5 Loops， Unitarity， and Analyticity5.1 Unitarity of the S Matrix5.2 The Analytic S Matrix5.2.1 Origin of Analyticity5.2.2 Unitarity and Branch Cuts5.2.3 Resonances， Widths， and Lifetimes5.3 Some Loop Diagrams5.3.1 Wick Rotation5.3.2 Feynman Parameters5.3.3 Dimensional Regularization6 Formal Developments6.1 Gell-Mann Low Theorem6.2 Lehmann-Kaillen Spectral Representation6.3 LSZ Reduction Formulae6.3.1 Amputation of External Legs6.3.2 In and Out States and Fields6.3.3 Borchers Classes7 Fermions7.1 Dirac Equation7.2 Spinors， Tensors， and Currents7.2.1 Field Bilinears7.2.2 Conservation Laws7.3 Holes and the Dirac Sea7.3.1 Positive and Negative Energies7.3.2 Holes7.4 Quantization7.4.1 Normal and Time-Ordered Products8 QED8.1 Quantizing Maxwells Equations8.1.1 1 Hamiltonian Formalism8.1.2 Axial Gauge8.1.3 Lorentz Gauge8.2 Feynman Rules for QED8.2.1 Moiler Scattering8.3 Ward Identity and Gauge Invariance8.3.1 The Ward Identity8.3.2 Applications9 Electrons in Solids9.1 Second Quantization9.2 Fermi Gas and Fermi Liquid9.2.1 One-Particle Density Matrix9.2.2 Linear Response9.2.3 Diagram Approach9.2.4 Applications9.3 Electrons and Phonons10 Nonrelativistic Bosons10.1 The Boson Field10.2 Spontaneous Symmetry Breaking10.3 Dilute Bose Gas10.3.1 Bogoliubov Transfomation10.3.2 Field Equations10.3.3 Quantization10.3.4 Landau Criterion for Superfiuidity10.3.5 Normal and Superfiuid Densities10.4 Charged Bosom10.4.1 Gross-Pitaevskii Equation10.4.2 Vortices10.4.3 Connection with Fluid Mechanics11 Finite Temperature11.1 Partition Functions11.2 Worldlines11.3 Matsubara Sums12 Path Integrals12.1 Quantum Mechanics of a Particle12.1.1 Real Time12.1.2 Euclidean Time12.2 Gauge Invariance and Operator Ordering12.3 Correlation Functions12.4 Fields12.5 Gaussian Integrals and Free Fields12.5.1 Real Fields12.5.2 Complex Fields12.6 Perturbation Theory13 Functional Methods13.1 Generating Functionals13.1.1 Effective Action13.2 Ward Identities13.2.1 Goldstones Theorem14 Path Integrals for Fermions14.1 Berezin Integrals14.1.1 A Simple Supersymmetry14.2 Fermionic Coherent States14.3 Superconductors14.3.1 Effective Action15 Lattice Field Theory15.1 Boson Fields15.2 Random Walks15.3 Interactions and Bose Condensation15.3.1 Rotational Invariance15.4 Lattice Fermions15.4.1 No Chiral Lattice Fermions16 The Renormailzation Group16.1 Transfer Matrices16.1.1 Continuum Limit16.1.2 Two-Dimensional Ising Model16.2 Block Spins and Renormalization Group16.2.1 Correlation Functions17 Fields and Renormalization17.1 The Free-Field Fixed Point17.2 The Gaussian Model17.3 General Method17.4 Nonlinear o Model17.4.1 Renormalizing17.4.2 Solution of the RGE17.5 Renormalizing18 Large N Expansions18.1 O(N) Linear a-Model18.2 Large N Expansions18.2.1 Linear vs. Nonlinear σ-ModelsA Relativistic State NormalizationB The General CommutatorC Dimensional RegularizationC.I Analytic Continuation and IntegralsC.2 PropagatorsD Spinors and the Principle of the SextantD.1 Constructing the λ-MatricesD.2 Basic TheoremD.3 ChiralityD.4 Spin(2N)， Pin(2N)， and SU(N) C SO(2N)E Indefinite MetricF Phonons and MomentumG Determinants in Quantum MechanicsIndex

作者简介

《量子场物理学》is intended to provide a general introduction to the physics of quantized fields and many-body physics. It is based on a two-semester sequence of courses taught at the University of Illinois at Urbana-Champaign at various times between 1985 and 1997. The students taking all or part of the sequence had interests ranging from particle and nuclear theory through quantum optics to condensed matter physics experiment.

The book does not cover as much ground as some texts. This is because I have tried to concentrate on the basic conceptual issues that many students find difficult. For a computation-method oriented course an instructor would probably wish to suplement this book with a more comprehensive and specialized text such as Peskin and Schroeder An Introduction to Quantum Field Theory, which is intended for particle theorists, or perhaps the venerable Quantum Theory of Many-Particle Systems by Fetter and Walecka.

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