規(guī)范場理論

內(nèi)容概要

This book has its origin in a long series of lectures given at the Institute for Theoretical Physics, Warsaw University. It is addressed to graduate students and to young research workers in theoretical physics who have some knowledge of quantum field theory in its canonical formulation, for instance at the level of two volumes by Bjorken & Drell (1964, 1965). The book is intended to be a relatively concise reference to some of the field theoretical tools used in contemporary research in the theory of fundamental interactions. It is a technical book and not easy reading. Physical problems are discussed only as illustrations of certain theoretical ideas and of computational methods. No attempt has been made to review systematically the present status of the theory of fundamental interactions.

作者簡介

作者：(波蘭)波考斯(Pokorski S.)

書籍目錄

Preface to the First Edition 0 Introduction   0.1 Gauge invariance   0.2 Reasons for gauge theories of strong and electroweak interactions 　　QCD 　　Electroweak theory 1 Classical fields, symmetries and their breaking 　1.1 The action, equations of motion, symmetries and conservation laws 　　Equations of motion 　　Global symmetries 　　Space-time transformations 　　Examples 　1.2 Classical field equations 　　Scalar field theory and spontaneous breaking of global symmetries 　　Spinor fields 　1.3 Gauge field theories 　　U(1) gauge symmetry 　　Non-abelian gauge symmetry   1.4 From Classical to quantum fields (canonical quantization)　  Scalar fields  　The Feynman propagator　  Spinor fields  　Symmetry transformations for quantum ields    1.5 Discrete symmetries　  Space reflection  　Time reversal 　  Charge conjugation  　Summary and the CPT transformations　  CP violation in the neutral K0-K0-system    　Problems2 Path integral formulation of quantum field theory　2.1 Path integrals in quantum mechanics　　Transition matrix elements as path integrals　　Matrix elements of position operators　2.2 Vacuum-to-vacuum transitions and the imaginary time formalism　　General discussion　　Harmonic oscillator　　Euclidean Green's functions　2.3 Path integral formulation of quantum field theory　　Green's functions as path integrals　　Action quadratic in fields　　Gaussian integration　2.4 Introduction to perturbation theory　　Perturbation theory and the generating functional　　Wick's theorem　　An example: four-point Green's function in λφ4　　Momentum space　2.5 Path integrals for fermions; Grassmann algebra　　Anticommuting c-numbers　　Dirac propagator　2.6 Generating functionals for Green's functions and proper vertices; effective　　potential　　Classification of Green's functions and generating functionals　　Effective action　　Spontaneous symmetry breaking and effective action　　Effective potential　2.7 Green's functions and the scattering operator　　Problems3 Feynman rules for Yang-Mills theories　3.1 The Faddeev-Popov determinant　　Gauge invariance and the path integral　　Faddeev-Popov determinant　　Examples　　Non-covariant gauges　3.2 Feynman rules for QCD　　Calculation of the Faddeev-Popov determinant　　Feynman rules　3.3 Unitarity, ghosts, Becchi-Rouet-Stora transformation　　Unitarity and ghosts　　BRS and anti-BRS symmetry　　Problems4 Introduction to the theory of renormalization　4.1 Physical sense of renormalization and its arbitrariness　　Bare and 'physical' quantities　　Counterterms and the renormalization conditions　……5 Quantum electrodynamics6 Renormalization group7 Scale invariance and operator product expansion8 Quantum chromodynamics9 Chiral symmetry; spontaneous symmetry breading10 Spontaneous and explicit global symmetry breaking11 Brout-Englert-Higgs mechanism in gauge theories12 Standard electroweak theory13 Chiral anomalies14 Effective lagrangians15 Introduction to supersymmetryAppendix A: Spinors and their propertiesAppendix B: Feynman rules for QED and QCD and Feynman integralsAppendix C: Feynman rules for the Standard ModelAppendix D: One-loop Feynman integralsAppendix E: Elements of group theoryReferencesIndex

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