Finite Quantum Electrodynamics: The Causal Approach, Third Edition

Finite Quantum Electrodynamics: The Causal Approach, Third Edition

by Gunter Scharf

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Overview

In this classic text for advanced undergraduates and graduate students of physics, author Günter Scharf carefully analyzes the role of causality in quantum electrodynamics. His approach offers full proofs and detailed calculations of scattering processes in a mathematically rigorous manner. This third edition contains Scharf's revisions and corrections plus a brief new Epilogue on gauge invariance of quantum electrodynamics to all orders.
The book begins with Dirac's theory, followed by the quantum theory of free fields and causal perturbation theory, a powerful method that avoids ultraviolet divergences and solves the infrared problem by means of the adiabatic limit. Successive chapters explore properties of the S-matrix — such as renormalizability, gauge invariance, and unitarity — the renormalization group, and interactive fields. Additional topics include electromagnetic couplings and the extension of the methods to non-abelian gauge theories. Each chapter is supplemented with problems, and four appendixes conclude the text.

Product Details

ISBN-13: 9780486782287
Publisher: Dover Publications
Publication date: 03/07/2014
Series: Dover Books on Physics
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 432
File size: 96 MB
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Table of Contents

0 Preliminaries 1

0.0 Historical Introduction 1

0.1 Minkowski Space and the Lodrentz Group 6

0.2 Tensors in Minkowski Space 11

0.3 Some Topics of Scattering Theory 14

0.4 Problems 19

1 Relativistic Quantum Mechanics 21

1.1 Spinor Representations of the Lorentz Group 21

1.2 Invariant Field Equations 26

1.3 Algebraic Properties of the Dirac Equation 32

1.4 Discussion of the Free Dirac Equation 36

1.5 Gauge Invariance and Electromagnetic Fields 44

1.6 The Hydrogen Atom 54

1.7 Problems 62

2 Field Quantization 66

2.1 Second Quantization in Fock Space 67

2.2 Quantization of the Dirac Field 78

2.3 Discussion of the Commutation Functions 87

2.4 The Scattering Operator (S-Matrix) in Fock Space 93

2.5 Perturbation Theory 105

2.6 Electron Scattering 111

2.7 Pair Production 118

2.8 The Causal Phase of the S-Matrix 124

2.9 Non-perturbative Construction of the Causal Phase 134

2.10 Vacuum Polarization 141

2.11 Quantization of the Radiation Field 146

2.12 Problems 156

3 Causal Perturbation Theory 159

3.1 The Method of Epstein and Glaser 160

3.2 Splitting of Causal Distributions 171

3.3 Application to QED 185

3.4 Electron Scattering (Moeller Scattering) 188

3.5 Electron-Photon Scattering (Compton Scattering) 197

3.6 Vacuum Polarization 204

3.7 Self-Energy 210

3.8 Vertex Function: Causal Distribution 217

3.9 Vertex Function: Retarded Distribution 231

3.10 Form Factors 239

3.11 Adiabatic Limit 242

3.12 Charged Particles in Perturbative QED 250

3.13 Charge Normalization 260

3.14 Problems 263

4 Properties of the S-Matrix 266

4.1 Vacuum Graphs 266

4.2 Operator Character of the S-Matrix 271

4.3 Normalizability of QED 274

4.4 Discreté Symmetries 279

4.5 Poincaré Covariance 286

4.6 Gauge Invariance and Ward Identities 293

4.7 Unitarity 304

4.8 Renormalization Group 312

4.9 Interacting Fields and Operator Products 318

4.10 Field Equations 327

4.11 Problems 337

5 Other Electromagnetic Couplings 338

5.1 Scalar QED: Basic Properties 338

5.2 Scalar QED: Gauge Invariance 347

5.3 Axial Anomalies 354

5.4 2+1-Dimensional QED: Vacuum Polarization 365

5.5 2+1-Dimensional QED: Mass Generation 372

5.6 Problems 378

6 Epilogue

6.1 Non-abelian Gauge Theories 379

6.2 Gauge Invariance of QED to all Orders 382

Appendices

A The Hydrogen Atom According to the Schrodinger Equation 386

B Regularly Varying Functions 389

C Spence Functions 394

D Grassmann Test Functions 397

Bibliographical Notes 402

Subject Index 409

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