Functional Analysis and the Feynman Operator Calculus

✍ Scribed by Tepper L. Gill, Woodford W. Zachary (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 370
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xix
Preliminary Background....Pages 1-48
Integration on Infinite-Dimensional Spaces....Pages 49-107
HK-Integral and HK-Spaces....Pages 109-150
Analysis on Hilbert Space....Pages 151-191
Operators on Banach Space....Pages 193-235
Spaces of von Neumann Type....Pages 237-274
The Feynman Operator Calculus....Pages 275-313
Applications of the Feynman Calculus....Pages 315-346
Back Matter....Pages 347-354

✦ Subjects

Functional Analysis; Mathematical Methods in Physics; Operator Theory