Relativistic Quantum Field Theory, Volume 1

Canonical formalism

By (author) Michael Strickland Series edited by Julia Velkovska

Publication date:

07 November 2019

Publisher

Morgan & Claypool Publishers

ISBN-13: 9781643277011

BOOK DESCRIPTION
TABLE OF CONTENTS

Volume 1 of this three-part series introduces the fundamental concepts of quantum field theory using the formalism of canonical quantization. This volume is intended for use as a text for an introductory quantum field theory course that can include both particle and condensed matter physics students. Starting with a brief review of classical field theory as a jumping off point for the quantization of classical fields, thereby promoting them to proper quantum fields, formalism for real and complex scalar field theories is then presented, followed by fermion field quantization, gauge field quantization, toy models of the nuclear interaction, and finally the full Lagrangian for QED and its renormalization.

1 Classical Field Theory

1.1 Lagrangian formalism for fields

1.2 The Klein-Gordon field

1.3 The electromagnetic field

1.4 Lorentz invariance

1.5 Transformation of fields under Lorentz transformations

1.6 Noether’s theorem

1.7 Applications of Noether’s theorem

1.8 The Hamiltonian formalism for fields

2 Quantization of free fields

2.1 The quantum linear chain and phonons

2.2 Poisson brackets in classical field theory

2.3 Quantization of a free scalar field theory

2.4 Multi-particle states and Fock space

2.5 Complex Scalar Fields

2.6 Quantization of a complex scalar field

2.7 Causality

2.8 Propagators

2.9 Propagators as Green’s functions

3 Interacting field theories

3.1 Weakly-interacting scalar fields

3.2 Two examples of interacting quantum field theories

3.3 The interaction picture and Dyson’s equation

3.4 Interactions in scalar Yukawa theory

3.5 The S-matrix

3.6 Beyond leading-order perturbation theory

3.6.1 Wick’s Theorem

3.6.2 Feynman diagrams

3.6.3 Feynman diagrams for scalar λ φ4 theory

3.6.4 Wick rotation

3.7 Decay rates and cross sections

3.8 Examples using scalar Yukawa theory

4 Quantum Electrodynamics

4.1 Classical Dirac fields

4.2 Quantization of the Dirac field

4.3 The Feynman propagator for Dirac fields

4.4 The electromagnetic field

4.5 Quantization of the electromagnetic field

4.6 Coupling the electron to the photon

4.7 QED Feynman rules

4.8 QED Feynman rules – Examples

5 Renormalization of Quantum Electrodynamics

5.1 Renormalization group flow

5.2 Beta functions

5.3 Renormalizable field theories

5.4 Dimensional regularization in QED

5.5 One-loop renormalization of QED

5.6 Schwinger-Dyson equations

5.7 Photon wavefunction renormalization

5.8 Electron wavefunction and mass renormalization

5.9 Vertex renormalization

5.10 The renormalized QED Lagrangian

5.11 The one-loop QED running coupling

A Classical mechanics review

A.1 Lagrangian mechanics

A.2 Hamiltonian mechanics

A.3 Poisson brackets

A.4 Classical mechanics with many degrees of freedom

B Functionals and functional derivatives

C Tensor algebra

D Mandelstam variables