Introduction to Quantum Field Theory 2nd Edition by Roberto Casalbuoni 9813146664 9789813146662

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ISBN 10: 9813146664

ISBN 13: 9789813146662

Author: Roberto Casalbuoni

This book deals with quantum field theory, the language of modern elementary particles physics. Based on university lectures given by the author, this volume provides a detailed technical treatment of quantum field theory that is particularly useful for students; it begins with the quantization of the most important free fields, the scalar, the spin-1/2 and the photon fields, and is then followed by a detailed account of symmetry properties, including a discussion on global and local symmetries and the spontaneous breaking of symmetries. Perturbation theory, one-loop effects for quantum electrodynamics, and renormalization properties are also covered. In this second edition new chapters have been introduced with a general description of path integral quantization both on quantum mechanics and in quantum field theory, with a particular attention to the gauge fields. The path integral quantization of Fermi fields is also discussed.

Introduction to Quantum Field Theory 2nd Table of contents:

1. Introduction

1.1 Notation and units

1.2 Major steps in quantum field theory

1.3 The Lorentz group

1.4 Spinor representations of the Lorentz group

1.5 The Poincaré group

1.6 Exercises

2. Lagrangian formalism for continuum systems and quantization

2.1 Many degrees of freedom

2.2 Linear atomic string

2.3 String quantization

2.4 The canonical formalism for continuum systems

2.5 The canonical quantization of a continuum system

2.6 Exercises

3. The Klein-Gordon field

3.1 The problems in relativistic quantum mechanics

3.2 Quantization of the Klein-Gordon field

3.3 Noether’s theorem for relativistic fields

3.4 Energy and momentum of the Klein-Gordon field

3.5 Locality and causality in field theory

3.6 The charged scalar field

3.7 Exercises

4. The Dirac field

4.1 The Dirac equation

4.2 Covariance properties of the Dirac equation

4.3 The Dirac equation and the Lorentz group

4.4 Free particle solutions of the Dirac equation

4.5 Wave packets and negative energy solutions

4.6 Electromagnetic interaction of a relativistic point-like particle

4.7 Nonrelativistic limit of the Dirac equation

4.8 Charge conjugation, time reversal and PCT transformations

4.9 Dirac field quantization

4.10 Massless spin 1/2 particles

4.11 Exercises

5. Vector fields

5.1 The electromagnetic field

5.2 Quantization of the electromagnetic field

5.3 Massive vector fields

5.4 Exercises

6. Symmetries in field theories

6.1 The linear σ-model

6.2 Spontaneous symmetry breaking

6.3 The Goldstone theorem

6.4 QED as a gauge theory

6.5 Non-abelian gauge theories

6.6 The Higgs mechanism

6.7 Exercises

7. Time ordered products

7.1 Time ordered products and propagators

7.2 A physical application of the propagators

7.3 Exercises

8. Perturbation theory

8.1 The electromagnetic interaction

8.2 The scattering matrix

8.3 Wick’s theorem

8.4 Evaluation of the S matrix at second order in QED

8.5 Feynman diagrams in momentum space

8.6 Exercises

9. Applications

9.1 The cross-section

9.2 The scattering e+e− → μ+μ−

9.3 Coulomb scattering

9.4 Application to atomic systems

9.5 Exercises

10. One-loop renormalization

10.1 Divergences of the Feynman integrals

10.2 Dimensional regularization of the Feynman integrals

10.3 Integration in arbitrary dimensions

10.4 One-loop regularization of QED

10.5 One-loop renormalization

10.6 Lamb shift and g − 2

10.7 Exercises

11. Path integral formulation of quantum mechanics

11.1 Feynman’s formulation of quantum mechanics

11.2 Path integral in configuration space

11.3 The physical interpretation of the path integral

11.4 Functional formalism

11.5 General properties of the path integral

11.6 The generating functional of Green’s functions

11.7 The Green function for the harmonic oscillator

11.8 Exercises

12. The path integral in field theory

12.1 In- and out-states

12.2 The S matrix

12.3 The reduction formalism

12.4 The path integral for a free scalar field

12.5 The perturbative expansion for the theory λφ4

12.6 The Feynman rules in momentum space

12.7 Regularization in λφ4

12.8 Renormalization in λφ4

12.9 Fermionic oscillators and Grassmann algebras

12.10 Properties of the integration over Grassmann variables

12.11 The path integral for the fermionic theories

12.12 Exercises

13. The quantization of the gauge fields

13.1 Path integral quantization of the gauge theories

13.2 Path integral quantization of QED

13.3 Path integral for the non-abelian gauge theories

13.4 Ward-Takahashi identities and anomalies

13.5 Exercises

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