Functional Integration: Action and Symmetries

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  • Edition: Revised
  • Format: Paperback
  • Copyright: 2010-06-10
  • Publisher: Cambridge University Press
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Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a new approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharanov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.

Table of Contents

List symbols, conventions, and formulary
The Physical and Mathematical Environment
The physical and mathematical environment
Quantum Mechanics
First lesson: gaussian integrals
Selected examples
Semiclassical expansion: WKB
Semiclassical expansion: beyond WKB
Quantum dynamics: path integrals and operator formalism
Methods from Differential Geometry
Grassmann analysis: basics
Grassmann analysis: applications
Volume elements, divergences, gradients
Non-Gaussian Applications
Poisson processes in physics
A mathematical theory of Poisson processes
First exit time: energy problems
Problems in Quantum Field Theory
Renormalization 1: an introduction
Renormalization 2: scaling
Renormalization 3: combinatorics
Volume elements in quantum field theory Bryce DeWitt
Forward and backward integrals: spaces of pointed paths
Product integrals
A compendium of gaussian integrals
Wick calculus Alexander Wurm
The Jacobi operator
Change of variables of integration
Analytic properties of covariances
Feynman's checkerboard
Table of Contents provided by Publisher. All Rights Reserved.

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