Feynman Path Integrals: Proceedings of the International Colloquium Held in Marseille, May 1978

by Sergio Albeverio (Editor), P. Combe (Editor), Raphael Høegh-Krohn (Editor)

Feynman path integrals and the corresponding method of stationary phase.- Processus de sauts et leurs applications dans la mecanique quantique.- The polygonal path formulation of the Feynman path integral.- Weyl quantization of classical spin systems quantum spins and Fermi systems.- Feynman path integral and theory of forms.- Caracterisation de processus par la methode des specifications locales.- Renormalization group approach to the hierarchical model.- Spinning particles and relativistic particles in the framework of Nelson's stochastic mechanics.- Construction of a class of characteristic functionals.- Topics on euclidean classical field equations with unique vacuua.- Null plane fields and automodel random processes.- Deformations et quantification.- Geometric quantisation and the Feynman integral.- Algebres tierces.- A reasonable method for computing path integrals on curved spaces.- Correspondence rules and path integrals.- Feynman-type integrals defined in terms of general cylindrical approximations.- Bounds on the Euclidean functional determinant.- Application of path integrals to non-perturbative study of massive Yang-Mills theory.- F = * F , A review.- Quartic oscillator.- Perturbation theory at large orders.- Anomalous behaviour of the effective potential.- Non-affine path algorithm in the functional integral calculus of Schrödinger kernels.- Non-Uniqqueness in writing Schrodinger kernel as a functional integral.- About the conformal properties of Yang-Mills fields.- Infrared problem and zero-mass limit in a model of non-abelian gauge theory.- Unitarity restrictions on semi-classical approximations to certain functional integrals.- On the Fokker-Planck Lagrangian.- Distribution definition of path integrals.- Functional integral representations and inequalities for bose partition functions.- Renormalization of Yang-Mills theory developed around an instanton.

463 pages, Paperback

First published September 14, 1979

About the author

Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.

He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.