The Feynman Integral and Feynmans Operational Calculus

Paperback | January 8, 2004

byGerald W. Johnson, Michel L. Lapidus

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This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the centralresults.

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This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discus...

Gerald W. Johnson is in the Department of Mathematics and Statistics, University of Nebraska-Lincoln. Michel L. Lapidus is in the Department of Mathematics, University of California, Riverside.

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Format:PaperbackDimensions:792 pages, 9.21 × 6.14 × 1.65 inPublished:January 8, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198515723

ISBN - 13:9780198515722

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Table of Contents

1. Introduction2. The physical phenomenon of Brownian motion3. Wiener measure4. Scaling in Wiener space and the analytic Feynman integral5. Stochastic processes and the Wiener process6. Quantum dynamics and the Schroedinger equation7. The Feynman integral: Heuristic ideas and mathematical difficulties8. Semigroups of operators: An informal introduction9. Linear semigroups of operators10. Unbounded self-adjoint operators and quadratic forms11. Product formulas with applications to the Feynman integral12. The Feynman-Kac formula13. Analytic-in-time or mass operator-valued Feynman integrals14. Feynman's operational calculus for noncommuting operators: An introduction15. Generalised Dyson series, the Feynman integral and Feynman's operational calculus16. Stability results17. The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus18. Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus19. Feynman's operational calculus and evolution equations20. Further work on or related to the Feynman integralReferencesIndex of symbolsAuthor indexSubject index

Editorial Reviews

`The second one [part of the final chapter] is a most welcome presentation of recent extensions and applications of Feynman's approach to a whole range of physical models of major interest ... it is here that the power of Feynman's approach of inspiring both mathematicans and physicists isbest evidentiated.'Zentrablatt Mathematik