Mazzucchi S. Mathematical Feynman Path Integrals and Their Applications

World Scientific Publishing Co. Pte. Ltd., 2009. — 225 p.The present book provides a detailed and self-contained description of the rigorous mathematical realization of Feynman path integrals in terms of infinite dimensional oscillatory integrals, a particular kind of functional integrals that can be recognized as the direct generalization of classical oscillatory integrals to the case where the integration is performed on an infinite dimensional space, in particular on a space of paths.
The book describes the mathematical dificulties, the first results obtained in the 70's and the 80's, as well as the more recent development and applications. Special attention has been paid to enlightening the mathematical techniques, including infinite dimensional integration theory,
asymptotic expansions and resummation techniques, without losing the connection with the physical interpretation of the theory.A large amount of references allows the reader to get a deeper knowledge of the most interesting mathematical results as well as of the modern physical applications.