Functional Integration: Action and Symmetries

Description

Functional integration successfully entered physics as path integrals in the 1942 PhD 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 fresh 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; Aharonov-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.

Emeritus Director of Research, Center National de la Recherche Scientifique, France. Member of Societe Francaise de Mathematiques and American Mathematical Society. Jane and Roland Blumberg Centennial Professor in Physics, Emerita, University of Texas at Austin. Member of American and European Physical Societies.

'...will be helpful for those mathematicians who are interested in physical applications of the general theory of measure (theory of integrals) and for the physicists who are interested in mathematically rigorous formulations of complicated problems in quantum physics.' Zentralblatt MATH