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GREEN'S FUNCTIONS AND ORDERED EXPONENTIALS
H.M. FRIED
CAMBRIDGE
UNIVERSITY PRESS 2002
djVu format
Preface
List of abbreviations
1 Introduction
1.1 Historical remarks
1.2 Linear Physics
2 Elementary functional methods
2.1 Functional differentiation
2.2 Linear translation
2.3 Quadratic (Gaussian) translation
2.4 Functional integration
2.5 Examples drawn from quantum field theory
2.6 Cluster decomposition
3 Schwinger-Fradkin methods
3.1 Proper-time representations of Schwinger and Fradkin
3.2 Fradkin representations for QED and QCD
3.3 Gauge structure in QED and QCD
3.4 Soluble examples: quadratic forms and perturbative
approximations
3.5 Pair production in generalized electric fields
4 Lasers and crossed lasers
4.1 Classical charged-particle propagation in a laser
(epw) field
4.2 The "scalar" laser solution for Gc[A]
4.3 The QED laser solutions for Gc[A] and L[A]
4.4 Pair production via crossed lasers
5 Special variants of the Fradkin representation
5.1 Exact representations for scalar interactions
5.2 Finite-quadrature approximations
5.3 Exact and approximate vectorial interactions
5.4 The Stojkov variation
6 Quantum chaos and vectorial interactions
6.1 First-quantization chaos
6.2 Chaos suppression in second quantization
6.3 Fluctuation-induced chaos suppression
7 Infrared approximations
7.1 The Bloch-Nordsieck approximation
7.2 IR damping at large momentum transfers
7.3 Eikonal scattering amplitudes in particle physics
7.4 IR approximations and rescaling corrections
to non-linear ODEs
8 Models of high-energy, non-Abelian scattering
8.1 An Abelian separation
8.2 The quasi-Abelian limit
8.3 Loop, ladder and crossed-ladder approximations
8.4 Summing all the eikonal graphs
9 Unitary ordered exponentials
9.1 Algebraic and differential structure
9.2 The SU(2) adiabatic limit
9.3 The stochastic limit
9.4 Functional integration over the stochastic limit
Index
170 Pages plus
H.M. FRIED
CAMBRIDGE
UNIVERSITY PRESS 2002
djVu format
Preface
List of abbreviations
1 Introduction
1.1 Historical remarks
1.2 Linear Physics
2 Elementary functional methods
2.1 Functional differentiation
2.2 Linear translation
2.3 Quadratic (Gaussian) translation
2.4 Functional integration
2.5 Examples drawn from quantum field theory
2.6 Cluster decomposition
3 Schwinger-Fradkin methods
3.1 Proper-time representations of Schwinger and Fradkin
3.2 Fradkin representations for QED and QCD
3.3 Gauge structure in QED and QCD
3.4 Soluble examples: quadratic forms and perturbative
approximations
3.5 Pair production in generalized electric fields
4 Lasers and crossed lasers
4.1 Classical charged-particle propagation in a laser
(epw) field
4.2 The "scalar" laser solution for Gc[A]
4.3 The QED laser solutions for Gc[A] and L[A]
4.4 Pair production via crossed lasers
5 Special variants of the Fradkin representation
5.1 Exact representations for scalar interactions
5.2 Finite-quadrature approximations
5.3 Exact and approximate vectorial interactions
5.4 The Stojkov variation
6 Quantum chaos and vectorial interactions
6.1 First-quantization chaos
6.2 Chaos suppression in second quantization
6.3 Fluctuation-induced chaos suppression
7 Infrared approximations
7.1 The Bloch-Nordsieck approximation
7.2 IR damping at large momentum transfers
7.3 Eikonal scattering amplitudes in particle physics
7.4 IR approximations and rescaling corrections
to non-linear ODEs
8 Models of high-energy, non-Abelian scattering
8.1 An Abelian separation
8.2 The quasi-Abelian limit
8.3 Loop, ladder and crossed-ladder approximations
8.4 Summing all the eikonal graphs
9 Unitary ordered exponentials
9.1 Algebraic and differential structure
9.2 The SU(2) adiabatic limit
9.3 The stochastic limit
9.4 Functional integration over the stochastic limit
Index
170 Pages plus