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.
作者簡(jiǎn)介
暫缺《量子場(chǎng)物理學(xué)》作者簡(jiǎn)介
圖書(shū)目錄
Preface 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 Convcntions 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 Noethers 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 Wicks Theorem 3.3.1 Normal Products 3.3.2 Wicks 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-Kaillen 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 Borchers 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 Maxwells Equations 8.1.1 1 Hamiltonian Formalism 8.1.2 Axial Gauge 8.1.3 Lorentz Gauge 8.2 Feynman Rules for QED 8.2.1 Moiler 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 Approach 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 Superfiuidity 10.3.5 Normal and Superfiuid Densities 10.4 Charged Bosom 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 Goldstones 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 Renormailzation 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 o Model 17.4.1 Renormalizing 17.4.2 Solution of the RGE 17.5 Renormalizing 18 Large N Expansions 18.1 O(N) Linear a-Model 18.2 Large N Expansions 18.2.1 Linear vs. Nonlinear σ-Models A Relativistic State Normalization B The General Commutator C Dimensional Regularization C.I Analytic Continuation and Integrals C.2 Propagators D Spinors and the Principle of the Sextant D.1 Constructing the λ-Matrices D.2 Basic Theorem D.3 Chirality D.4 Spin(2N)， Pin(2N)， and SU(N) C SO(2N) E Indefinite Metric F Phonons and Momentum G Determinants in Quantum Mechanics Index
鄂公網(wǎng)安備 42010302001612號(hào) 