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.
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