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Functional Analysis and the Feynman Operator Calculus

Authors: Gill, Tepper L., Zachary, Woodford W.

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  • Provides a mathematically rigorous formulation of both the path integral and the operator calculus in the manner intended by Feynman
  • Unifies the theory of partial differential equations with time-dependent coefficients using Feynman's theory
  • ​Provides the first introduction to Lebesgue integration on Banach spaces
  • Includes a direct approach to the study of time-dependent evolution equations in both finite and infinite-dimensional settings
  • Solves the second of the two open Dyson conjectures
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-27595-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-27593-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-80180-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

“The book is a self-contained treatise on the mathematical foundation of Feynman operational calculus and Feynman path integrals. … It contains a large amount of original material which cannot be found elsewhere in book form; in fact, most of the original results are due to the authors themselves. … The book will be of interest to both graduate students and researchers in pure or applied mathematics.” (Sonia Mazzucchi, Mathematical Reviews, November, 2016)

“This book carries Fujiwara's insight to provide the mathematical frameworks for Feynman's operator calculus and for the Feynman path integral. … The book is intended for advanced graduate students and researchers and can be used as a text for advanced courses in functional analysis, operator theory, mathematical physics, or related subjects.” (Miyeon Kwon, zbMATH 1345.81001, 2016)>

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-27595-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-3-319-27593-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.99
price for USA in USD
  • ISBN 978-3-319-80180-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Functional Analysis and the Feynman Operator Calculus
Authors
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-27595-6
DOI
10.1007/978-3-319-27595-6
Hardcover ISBN
978-3-319-27593-2
Softcover ISBN
978-3-319-80180-3
Edition Number
1
Number of Pages
XIX, 354
Number of Illustrations
3 illustrations in colour
Topics