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Functional analysis and the Feynman operator calculus / by Tepper Gill, Woodford Zachary.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Gill, Tepper., Author.
- Zachary, Woodford., Author.
- Language:
- English
- Subjects (All):
- Functional analysis.
- Physics.
- Operator theory.
- Functional Analysis.
- Mathematical Methods in Physics.
- Operator Theory.
- Local Subjects:
- Functional Analysis.
- Mathematical Methods in Physics.
- Operator Theory.
- Physical Description:
- 1 online resource (370 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- Preliminary Background
- Integration on Infinite-dimensional Spaces
- HK-Integral and HK-Spaces
- Analysis on Hilbert Space
- Operators on Banach Space
- Spaces of von Neumann Type
- The Feynman Operator Calculus
- Applications of the Feynman Calculus.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references at the end of each chapters and index.
- ISBN:
- 3-319-27595-X
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