Basics of Quantum Electrodynamics: 1st Edition (Hardback) book cover

Basics of Quantum Electrodynamics

1st Edition

By Ioan Merches, Dorian Tatomir, Roxana E. Lupu

CRC Press

352 pages | 13 B/W Illus.

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Hardback: 9781466580374
pub: 2012-12-05
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Description

Quantum electrodynamics (QED) is the branch of relativistic quantum field theory that deals specifically with the interactions between charged particles. It is widely used to solve problems in many areas of physics, such as elementary particles, atomic and molecular systems, and solid state physics. This accessible text, Basics of Quantum Electrodynamics, supplies a solid foundation in this dynamic area of physics, making a direct connection to the concepts of quantum mechanics familiar to the advanced undergraduate student.

Chapters cover the general theory of free fields and the quantization of the scalar, electromagnetic, and spinorial fields, which prepares readers for understanding field interactions. The authors describe the general theory of field interactions, introducing the scattering matrix and the Feynman–Dyson graphs. They then discuss divergence-free second-order processes, such as Compton and Møller scattering, followed by divergent second-order processes, which cover vacuum polarization and mass and charge renormalization.

Providing a modern, informative textbook, this volume illustrates the intimate connection between quantum mechanics and QED in two basic steps: the quantization of free fields, followed by the theory of their interactions. The text contains solved problems to facilitate the application of the theory, as well as a useful appendix on the theory of distributions. The step-by-step description of the quantization of various fields and the clear presentation of the most important interaction processes in QED make this textbook a useful guide for those studying physics at both the graduate and undergraduate level, as well as a reference for teachers and researchers in the field.

Table of Contents

General Field Theory

Basic field equations

Infinitesimal Lorentz Transformation

Transformation of the quantities U(r) in particular cases

Invariance of the Lagrangian density under infinitesimal Lorentz transformation

The energy-momentum tensor of a field

The angular momentum tensor of a field

Symmetry transformations

Phase transformations

General Problems of Field Quantization

Necessity of field quantization

Commutation and anti-commutation relations. Emission and absorption operators

Commutation relations and the Bose-Einstein statistics

Anti-commutation relations and the Fermi-Dirac statistics

Alternative methods of field quantization

Notations and units in QFT

The Quantization of the Scalar Field

The Lagrangian formalism

Momentum representation

Momentum, energy and charge of the complex scalar field in momentum representation

Commutators of the free scalar field

Products of operators

Vacuum states. The Fock representation

Wick’s theorems

The Quantization of the Electromagnetic Field

Lagrangian formalism

Momentum representation

Momentum, energy and spin of the electromagnetic field in momentum representation

Commutators of the free electromagnetic field

The indefinite metric formalism

The Lorentz-Fermi condition

The Quantization of the Spinorial Field

The Dirac equation and the algebra of gamma matrices

Lagrangian formalism

The free particle in the Dirac theory

Energy, momentum, charge and spin of the free spinorial field in momentum representation

Anti-commutators of the free spinorial field

Products of spinorial operators

General Problems of Field Interactions

Generalities

The S-matrix

Choice of the interaction Lagrangian density

The Feynman-Dyson diagrams

Examples of Feynman-Dyson diagrams

Transition probability

Scattering cross section

Non-Divergent Second-Order Processes

Transition probability for Compton scattering

Differential cross section for Compton scattering

Electron-positron annihilation

Transition probability for Møller scattering

Møller scattering cross section

Photon-photon scattering with electron-positron pair production

Electron-positron scattering

Divergent Second-Order Processes

Self-energy diagram of the electron

Self-energy diagram of the photon. The vacuum polarization

Mass and charge renormalization

Appendix. Distributions

Unidimensional delta function

Various representations of the delta function

Some functions related to delta

Functions Dm+ and Dm−

Functions Dm and ˜Dm

Functions D0, ˜D0, D0+, D0−

Functions S, ˜S, S+, S

Retarded and advanced functions

Causal functions

Problems with Solutions

References

Subject Index

About the Originator

Subject Categories

BISAC Subject Codes/Headings:
SCI013050
SCIENCE / Chemistry / Physical & Theoretical
SCI057000
SCIENCE / Quantum Theory