Green's Functions and Ordered Exponentials

✍ Scribed by H. M. Fried

• Publisher: Cambridge University Press
• Year: 2002
• Tongue: English
• Leaves: 182
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with new approximations for the treatment of color fluctuations in high-energy QCD scattering.

✦ Table of Contents

Contents......Page 8
Preface......Page 10
List of abbreviations......Page 12
1.1 Historical remarks......Page 14
1.2 Linear Physics......Page 16
1.3 Ordered exponentials......Page 26
Notes......Page 29
2.1 Functional differentiation......Page 30
2.2 Linear translation......Page 31
2.3 Quadratic (Gaussian) translation......Page 33
2.4 Functional integration......Page 36
2.5 Examples drawn from quantum field theory......Page 40
2.6 Cluster decomposition......Page 43
Notes......Page 45
3.1 Proper-time representations of Schwinger and Fradkin......Page 46
3.2 Fradkin representations for QED and QCD......Page 50
3.3 Gauge structure in QED and QCD......Page 53
3.4 Soluble examples: quadratic forms and perturbative approximations......Page 56
3.5 Pair production in generalized electric fields......Page 58
Notes......Page 63
4.1 Classical charged-particle propagation in a laser (epw) field......Page 64
4.2 The “scalar” laser solution for G[sub(c)][A]......Page 67
4.3 The QED laser solutions for G[sub(c)][A] and L[A]......Page 69
4.4 Pair production via crossed lasers......Page 75
Notes......Page 85
5.1 Exact representations for scalar interactions......Page 88
5.2 Finite-quadrature approximations......Page 95
5.3 Exact and approximate vectorial interactions......Page 100
5.4 The Stojkov variation......Page 103
Notes......Page 105
6.1 First-quantization chaos......Page 106
6.2 Chaos suppression in second quantization......Page 111
6.3 Fluctuation-induced chaos suppression......Page 114
Notes......Page 119
7 Infrared approximations......Page 120
7.1 The Block–Nordsieck approximation......Page 121
7.2 IR damping at large momentum transfers......Page 123
7.3 Eikonal scattering amplitudes in particle physics......Page 127
7.4 IR approximations and rescaling corrections to non-linear ODEs......Page 132
Notes......Page 136
8 Models of high-energy, non-Abelian scattering......Page 138
8.1 An Abelian separation......Page 139
8.2 The quasi-Abelian limit......Page 141
8.3 Loop, ladder, and crossed-ladder approximations......Page 146
8.4 Summing all the eikonal graphs......Page 155
Notes......Page 160
9.1 Algebraic and differential structure......Page 162
9.2 The SU(2) adiabatic limit......Page 163
9.3 The stochastic limit......Page 167
9.4 Functional integration over the stochastic limit......Page 176
Notes......Page 180
M......Page 181
Z......Page 182