Functional Integration and Quantum Physics (Pure and Applied Mathematics) - Hardcover

Simon, Barry

Hardcover

ISBN 10: 0126442509 ISBN 13: 9780126442502

Publisher: Academic Press Inc, 1979

Synopsis

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 Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), the author presents four different proofs of the Feynman-Kac formula. Also included is a simple exposition of stochastic Ito calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman-Kac-Ito formula). Among other topics discussed are the probabilistic approach to the bound of the number of ground states of correlation inequalities (the Birman-Schwinger principle, Lieb's formula, etc.), the calculation of asymptotics for functional integrals of Laplace type (the theory of Donsker-Varadhan) 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.

Edition details

• Publisher: Academic Press Inc
• Publication date: 1979
• Language: English
• ISBN 10: 0126442509
• ISBN 13: 9780126442502
• Binding: Hardcover
• Number of pages: 320