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Functional Analysis and the Feynman Operator Calculus
Buch von Woodford Zachary (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xix
354 S.
3 farbige Illustr.
354 p. 3 illus. in color.
ISBN-13: 9783319275932
ISBN-10: 3319275933
Sprache: Englisch
Herstellernummer: 978-3-319-27593-2
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Zachary, Woodford
Gill, Tepper
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 241 x 160 x 26 mm
Von/Mit: Woodford Zachary (u. a.)
Erscheinungsdatum: 08.04.2016
Gewicht: 0,729 kg
Artikel-ID: 104130860
Zusammenfassung

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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xix
354 S.
3 farbige Illustr.
354 p. 3 illus. in color.
ISBN-13: 9783319275932
ISBN-10: 3319275933
Sprache: Englisch
Herstellernummer: 978-3-319-27593-2
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Zachary, Woodford
Gill, Tepper
Auflage: 1st ed. 2016
Hersteller: Springer International Publishing
Springer International Publishing AG
Maße: 241 x 160 x 26 mm
Von/Mit: Woodford Zachary (u. a.)
Erscheinungsdatum: 08.04.2016
Gewicht: 0,729 kg
Artikel-ID: 104130860
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