Green's Functions and Ordered Exponentials

A detailed exposition, with applications to problems in potential theory and quantum field theory.

H. M. Fried (Author)

9780521443906, Cambridge University Press

Hardback, published 10 October 2002

182 pages, 29 b/w illus.
22.9 x 15.2 x 1.4 cm, 0.429 kg

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 approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.

Preface
1. Introduction
2. Elementary functional methods
3. Schwinger–Fradkin methods
4. Lasers and crossed lasers
5. Special variants of the Fradkin representation
6. Quantum chaos and vectorial interactions
7. Infrared approximations
8. Models of high-energy, non-Abelian scattering
9. Unitary ordered exponentials.

Subject Areas: Maths for engineers [TBJ], Physics [PH], Maths for scientists [PDE], Nonlinear science [PBWR]