ISBN: 3-540-67024-6
TITLE: Perturbative Quantum Electrodynamics and Axiomatic Field Theory
AUTHOR: Steinmann, Othmar
TOC:

1 Introduction 1
Part I What Is Quantum Electrodynamics?
2 Relativistic Covariance 7
2.1 The Lorentz Group 7
2.2 Representations 9
2.3 Covariant Fields 16
3 Electrodynamics as a Classical Field Theory 19
4 The Basic Principles of Relativistic Quantum Field Theory 25
4.1 The Wightman Axioms 25
4.2 The Wightman Functions32
5 Free Fields 39
5.1 The Hermitian Scalar Field 39
Relation to the Canonical Formalism 45
5.2 Dirac Spinors 47
5.3 The Electromagnetic Field 53
5.4 The Functions +, D+, and Related Functions 61
6 An Outline of Interacting QED 67
6.1 General Description. 67
6.2 Solving the Field Equations 73
6.3 Renormalization and the UV Problem 75
7 The Electric Charges 85
Part II Perturbation Theory
8 The Program of Perturbation Theory 95
8.1 The Problem. 95
(a) Equations of Motion 95
(b) W-Properties 97
(c) Renormalization Conditions 97
8.2 Perturbation Theory 98
8.3 Uniqueness 100
8.4 Time-Ordered Products 103
9 Unrenormalized Solution 109
9.1 Generalities 109
9.2 Special Examples in Low Orders110
9.3 The General Solution 115
Configuration Space 115
Momentum Space 120
9.4 Verifications 123
9.5 Current Conservation and the Charge Identity 131
10 Renormalization and the UV Problem 135
10.1 Low Orders 135
The Photon 2-Point Function 135
The Electron 2-Point Function 142
The Vertex Function 147
10.2 The General Case 151
10.3 Renormalization in Configuration Space 156
11 The IR Problem for Wightman Functions 165
11.1 The Problem. 165
11.2 The Solution 167
11.3 The W-Properties and Other Conditions 176
The W-Properties 176
The Charge Identity 178
Smoothness Conditions 180
12 Physical States 187
12.1 The General Strategy 187
12.2 Unrenormalized Perturbation Theory 192
12.3 The UV Problem 197
12.4 The IR Problem and the Final Verifications 201
Part III Particles and Their Reactions
13 The Standard View 213
13.1 Massive Theories 214
13.2 The IR Problem 217
14 Particle Probes 221
14.1 Mathematical Preliminaries 222
14.2 Free Particles 229
15 Interacting Particles 239
15.1 Probes for Interacting Particles. 239
15.2 IR Cancellations 246
Proof of Lemma 15.4 259
Proof of Theorems 15.13 265
15.3 Photons 272
Derivation of the Decomposition (15.87) 276
16 Reactions 283
16.1 Massive Scalar Fields 283
16.2 Reactions in QED 296
16.3 Photons 300
16.4 Electrons 304
17 Cross Sections 321
17.1 Cross Sections: the Problem 321
17.2 A Solution 330
17.3 Compton Scattering , an Example 336
References 347
Index 351
END
