Lectures on Classical and Quantum Theory of Fields

✍ Scribed by Leszek Hadasz Henryk Arod? Henryk Arodz, Leszek Hadasz

• Publisher: Springer Verlag
• Year: 2010
• Tongue: English
• Leaves: 354
• Category: Library

✦ Synopsis

This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

✦ Table of Contents

Lectures on Classical and QuantumTheory of Fields
Preface
Contents
Chapter 1 Introduction
1.1 Example A: Sinus-Gordon Effective Field
1.2 Example B: The Electromagnetic Field
1.3 Solutions of the Klein--Gordon Equation
Exercises
Chapter 2 The Euler--Lagrange Equations and Noether's Theorem
2.1 The Euler--Lagrange Equations
2.2 Noether's Theorem
Exercises
Chapter 3 Scalar Fields
3.1 The Lorentz and Poincaré Groups
3.2 The Real Scalar Field
3.3 The Complex Scalar Field
Exercises
Chapter 4 Vector Fields
4.1 The Abelian Gauge Field
4.2 Non-Abelian Gauge Fields
4.3 The Higgs Mechanism and a Massive Vector Field
Exercises
Chapter 5 Relativistic Spinor Fields
5.1 The Dirac Equation, Spin(4) and SL(2,C) Groups
5.2 The Dirac Field
5.3 The Weyl Fields
5.4 The Majorana Field
Exercises
Chapter 6 The Quantum Theory of Free Fields
6.1 The Real Scalar Field
6.2 The Dirac Field
6.3 The Electromagnetic Field
Exercises
Chapter 7 Perturbative Expansion in the bold0mu mumu Raw44 Model
7.1 The Gell-Mann--Low Formula
7.2 The Generating Functional for Green's Functions: Wick Formula
7.3 Feynman Diagrams in Momentum Space
Exercises
Chapter 8 Renormalization
8.1 Ultraviolet Divergences
8.2 The Example
8.3 BPHZ Subtractions
8.4 Renormalization of the 2-Point Green's Function
8.5 The Multiplicative Renormalization
Exercises
Chapter 9 Renormalization Group
9.1 Renormalization Group Equations
9.2 The Running Coupling Constant
9.3 Dimensional Transmutation
Exercises
Chapter 10 Relativistic Invariance and the Spectral Decomposition of bold0mu mumu G(2)G(2)RawG(2)G(2)G(2)G(2)
10.1 Relativistic Invariance in QFT
10.2 The Spectral Decomposition of G(2)
10.3 The Contribution of the Single Particle Sector
10.4 The Pole of the Perturbative (2)
Exercises
Chapter 11 Paths Integrals in QFT
11.1 Path Integrals in Quantum Mechanics
11.2 Path Integrals for Bosonic Fields
11.3 Path Integral for Fermionic Fields
Exercises
Chapter 12 The Perturbative Expansion for Non-Abelian Gauge Fields
12.1 The Faddeev--Popov--DeWitt Determinant
12.2 The Generating Functional for Green's Functions
12.3 Feynman Diagrams
12.4 BRST Invariance and Slavnov--Taylor Identities
Exercises
Chapter 13 The Simplest Supersymmetric Models
13.1 Simple Superalgebra
13.2 Supersymmetry Multiplets
13.3 Representation of Supersymmetry in a Space of Fields
13.4 The Superspace
13.5 The Wess--Zumino Model
13.6 Notation and Conventions
Exercises
Chapter 14 Anomalies
14.1 Simple Example of Anomaly
14.2 Anomalies and the Path Integral
Exercises
Appendix A Some Facts About Generalized Functions
Bibliography
Index