AMS Chelsea Publishing 2005; 306 pp; hardcover Volume: 351 ISBN10: 0821835823 ISBN13: 9780821835821 List Price: US$43 Member Price: US$38.70 Order Code: CHEL/351.H
 The main theme of this book is the "path integral technique" and its applications to constructive methods of quantum physics. The central topic is probabilistic foundations of the FeynmanKac formula. Starting with the main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the FeynmanKac formula. Also included is a simple exposition of stochastic Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the FeynmanKacItô formula). Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the BirmanSchwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of DonskerVaradhan) and applications, scattering theory, the theory of crushed ice, and the Wiener sausage. Written with great care and containing many highly illuminating examples, this classic book is highly recommended to anyone interested in applications of functional integration to quantum physics. It can also serve as a textbook for a course in functional integration. Readership Graduate students and research mathematicians interested in probability and applications of functional integration to quantum physics. Table of Contents  Introduction
 The basic processes
 Bound state problems
 Inequalities
 Magnetic fields and stochastic integrals
 Asymptotics
 Other topics
 References
 Index
 Bibliographic supplement
 Bibliography
