規範場理論

《規範場理論(第2版)》主要內容：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.

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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

Problems

2 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

Problems

3 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

Problems

4 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 electrodynamics

6 Renormalization group

7 Scale invariance and operator product expansion

8 Quantum chromodynamics

9 Chiral symmetry; spontaneous symmetry breading

10 Spontaneous and explicit global symmetry breaking

11 Brout-Englert-Higgs mechanism in gauge theories

12 Standard electroweak theory

13 Chiral anomalies

14 Effective lagrangians

15 Introduction to supersymmetry

Appendix A: Spinors and their properties

Appendix B: Feynman rules for QED and QCD and Feynman integrals

Appendix C: Feynman rules for the Standard Model

Appendix D: One-loop Feynman integrals

Appendix E: Elements of group theory

References

Index ^[2]