This 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.
General
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