Functional Analysis and the Feynman Operator Calculus

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Science, Physics, Mathematical Physics
Cover of the book Functional Analysis and the Feynman Operator Calculus by Tepper Gill, Woodford Zachary, Springer International Publishing
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Author: Tepper Gill, Woodford Zachary ISBN: 9783319275956
Publisher: Springer International Publishing Publication: March 30, 2016
Imprint: Springer Language: English
Author: Tepper Gill, Woodford Zachary
ISBN: 9783319275956
Publisher: Springer International Publishing
Publication: March 30, 2016
Imprint: Springer
Language: English

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.

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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.

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