Basics of Quantum Electrodynamics
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.

1133017919
Basics of Quantum Electrodynamics
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.

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Basics of Quantum Electrodynamics

Basics of Quantum Electrodynamics

Basics of Quantum Electrodynamics

Basics of Quantum Electrodynamics

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Overview

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.


Product Details

ISBN-13: 9780367380557
Publisher: Taylor & Francis
Publication date: 09/05/2019
Pages: 352
Product dimensions: 6.12(w) x 9.19(h) x (d)

About the Author

Merches, Ioan; Tatomir, Dorian; Lupu, Roxana E.

Table of Contents

Chapter I General Field Theory 1

1.1 Basic field equations 1

1.2 Infinitesimal Lorentz Transformation 5

1.3 Transformation of the quantities U(r) in particular cases 7

1.4 Invariance of the Lagrangian density under infinitesimal Lorentz transformation 12

1.5 The energy-momentum tensor of a field 13

1.6 The angular momentum tensor of a field 17

1.7 Symmetry transformations 20

1.8 Phase transformations 24

Chapter II General Problems of Field Quantization 27

2.1 Necessity of field quantization 27

2.2 Commutation and anti-commutation relations. Emission and absorption operators 32

2.3 Commutation relations and the Bose-Einstein statistics 36

2.4 Anti-commutation relations and the Fermi-Dirac statistics 41

2.5 Alternative methods of field quantization 43

2.6 Notations and units in QFT 46

Chapter III The Quantization of the Scalar Field 49

3.1 The Lagrangian formalism 49

3.2 Momentum representation 53

3.3 Momentum, energy and charge of the complex scalar field in momentum representation 58

3.4 Commutators of the free scalar field 64

3.5 Products of operators 71

3.6 Vacuum states. The Fock representation 74

3.7 Wick's theorems 77

Chapter IV The Quantization of the Electromagnetic Field 83

4.1 Lagrangian formalism 83

4.2 Momentum representation 86

4.3 Momentum, energy and spin of the electromagnetic field in momentum representation 89

4.4 Commutators of the free electromagnetic field 97

4.5 The indefinite metric formalism 100

4.6 The Lorentz-Fermi condition 102

Chapter V The Quantization of the Spinorial Field 109

5.1 The Dirac equation and the algebra of gamma matrices 109

5.2 Lagrangian formalism 115

5.3 The free particle in the Dirac theory 118

5.4 Energy, momentum, charge and spin of the free spinorial field in momentum representation 130

5.5 Anti-commutators of the free spinorial field 136

5.6 Products of spinorial operators 140

Chapter VI General Problems of Field Interactions 143

6.1 Generalities 143

6.2 The S-matrix 144

6.3 Choice of the interaction Lagrangian density 149

6.4 The Feynman-Dyson diagrams 152

6.5 Examples of Feynman-Dyson diagrams 156

6.6 Transition probability 164

6.7 Scattering cross section 167

Chapter VII Non-Divergent Second-Order Processes 173

7.1 Transition probability for Compton scattering 173

7.2 Differential cross section for Compton scattering 184

7.3 Electron-positron annihilation 189

7.4 Transition probability for Møller scattering 198

7.5 Møller scattering cross section 210

7.6 Photon-photon scattering with electron-positron pair production 220

7.7 Electron-positron scattering 232

Chapter VIII Divergent Second-Order Processes 241

8.1 Self-energy diagram of the electron 241

8.2 Self-energy diagram of the photon. The vacuum polarization 256

8.3 Mass and charge renormalization 269

Appendix. Distributions 273

A.1 Unidimensional delta function 273

A.2 Various representations of the delta function 275

A.3 Some functions related to delta 277

A.4 Functions Dm+ and Dm- 281

A.5 Functions Dm and Dm 283

A.6 Functions D0, D0, D0+, D0 286

A.7 Functions S, S, S+, S… 288

A.8 Retarded and advanced functions 289

A.9 Causal functions 293

Problems with Solutions 295

References 329

Subject Index 332

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