Functional Integration: Action and Symmetries

by Pierre Cartier , Cecile DeWitt-Morette

• ISBN13: 9780521143578
• ISBN10: 0521143578
• Edition: Revised
• Format: Paperback
• Copyright: 2010-06-10
• Publisher: Cambridge University Press

Summary

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

Acknowledgements

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

Symmetries

Homotopy

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

Projects

Projects

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

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.