Functional Integration And Quantum Physics (Ams Chelsea Publishing)

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 the 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. 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 the 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 Itô calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman–Kac–Itô 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. This work makes path integrals available as a tool to practicing mathematical physicists, and will open up new areas of research to probabilists. Coverage progresses from basic processes through bound state problems, inequalities, magnetic fields and stochastic integrals, and asymptotics. Simon has lectured in physics at the University of Geneva, Switzerland. This second edition includes brief bibliographic notes reflecting developments taking place in the field over the past 30 years. Annotation 2004 Book News, Inc., Portland, OR (booknews.com)