Feynman's Operational Calculus and Beyond
Noncommutativity and Time-Ordering
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher OUP Oxford
- Date of Publication 6 August 2015
- ISBN 9780198702498
- Binding Hardback
- No. of pages384 pages
- Size 236x165x25 mm
- Weight 664 g
- Language English 0
Categories
Short description:
This book lies at the interface between mathematics and quantum theory. It provides a mathematically precise development of certain heuristic ideas originated by Richard Feynman in a profoundly influential 1951 paper.
MoreLong description:
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book.
The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted.
This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.
Table of Contents:
Introduction
Disentangling: Definitions, Properties and Elementary Examples
Disentangling via Tensor Products and Ordered Supports
Extraction of Multilinear Factors and Iterative Disentangling
Auxiliary Operations and Disentangling Algebras
Time-Dependent Feynman's Operational Calculus and Evolution Equations
Stability Properties of Feynman's Operational Calculi
Disentangling via Continuous and Discrete Measures
Derivational Derivatives and Feynman's Operational Calculi
Spectral Theory for Noncommuting Operators
Epilogue: Miscellaneous Topics and Possible Extensions
