Gill T.L., Zachary W.W. Functional Analysis and the Feynman Operator Calculus

Springer International Publishing, Switzerland, 2016. — 370 p. — ISBN: 3319275933This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.Preliminary Background
Integration on Infinite-Dimensional Spaces
HK-Integral and HK-Spaces
Analysis on Hilbert Space
Operators on Banach Space
Spaces of von Neumann Type
The Feynman Operator Calculus
Applications of the Feynman Calculus