Functional Analysis and the Feynman Operator Calculus

Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-80180-3
Verlag: Springer International Publishing

Buch, Englisch, 354 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 5679 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Zachary, Woodford

Gill, Tepper

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

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.