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Functional Analysis and the Feynman Operator Calculus

  • Tepper L. Gill
  • Woodford W. Zachary

Table of contents

  1. Front Matter
    Pages i-xix
  2. Tepper L. Gill, Woodford Zachary
    Pages 1-48
  3. Tepper L. Gill, Woodford Zachary
    Pages 49-107
  4. Tepper L. Gill, Woodford Zachary
    Pages 109-150
  5. Tepper L. Gill, Woodford Zachary
    Pages 151-191
  6. Tepper L. Gill, Woodford Zachary
    Pages 193-235
  7. Tepper L. Gill, Woodford Zachary
    Pages 237-274
  8. Tepper L. Gill, Woodford Zachary
    Pages 275-313
  9. Tepper L. Gill, Woodford Zachary
    Pages 315-346
  10. Back Matter
    Pages 347-354

About this book

Introduction

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.

Keywords

Dyson Conjectures Feynman Integral Feynman Operator Calculus Lebesgue Integral on Banach Spaces Henstock-Kurzweil integral Adjoint operators on Banach spaces Jones spaces

Authors and affiliations

  • Tepper L. Gill
    • 1
  • Woodford W. Zachary
    • 2
  1. 1.Howard UniversityWashingtonUSA
  2. 2.Dept. of Electrical & Computer Eng.Howard UniversityWashingtonUSA

Bibliographic information