Table of Contents

1: Introduction
2: The physical phenomenon of Brownian motion
3: Wiener measure
4: Scaling in Wiener space and the analytic Feynman integral
5: Stochastic processes and the Wiener process
6: Quantum dynamics and the Schroedinger equation
7: The Feynman integral: Heuristic ideas and mathematical difficulties
8: Semigroups of operators: An informal introduction
9: Linear semigroups of operators
10: Unbounded self-adjoint operators and quadratic forms
11: Product formulas with applications to the Feynman integral
12: The Feynman-Kac formula
13: Analytic-in-time or mass operator-valued Feynman integrals
14: Feynman's operational calculus for noncommuting operators: An introduction
15: Generalised Dyson series, the Feynman integral and Feynman's operational calculus
16: Stability results
17: The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus
18: Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus
19: Feynman's operational calculus and evolution equations
20: Further work on or related to the Feynman integral
References
Index of symbols
Author index
Subject index

Reviews

`Review from previous edition:
Accessible, even for beginners ... this book should serve as a standard reference for anybody interested in the mathematical theory of Feynman path integrals and the related operational calculus.'
EMS
`Review from previous edition: The last chapter deals with other work related to the book's topics, ranging from alternative approaches to the path integral (so-called Fresnel integrals) to a very readable survey of the influence of Feynman integrals on contempary mathematics and physics. In particular, the authors discuss low dimensional topology and Edward Witten's approach to knot invariants, and they end with a
discussion of Maxim Kontsevich's work on deformation quantization. I would recommend this book to serious students of the subject.'
Physics Today
`The second one [part of the final chapter] is a most welcome presentation of recent extensions and applications of Feynman's approach to a whole range of physical models of major interest ... it is here that the power of Feynman's approach of inspiring both mathematicans and physicists is best evidentiated.'
Zentrablatt Mathematik