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.

Review of the hardback:'…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.'

Source: Zentralblatt MATH

Review of the hardback:'…for someone who is interested in the mathematical foundations or merely curious to see some of the deep insight of two true experts, Cartier and DeWitt-Morette's book is well worth reading.'

Source: Physics Today