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基本説明
New in paperback. Hardcover was published in 2000. The most comprehensive mathematical treatment to date of the Feynman path integral.
Full Description
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 central results.
Contents
1. Introduction ; 2. The physical phenomenon of Brownian motion ; 3. Wiener measure ; 4. Scaling in Wiener space and the analytic Feynman integral ; 5. Stochastic processes and the Wiener process ; 6. Quantum dynamics and the Schroedinger equation ; 7. The Feynman integral: Heuristic ideas and mathematical difficulties ; 8. Semigroups of operators: An informal introduction ; 9. Linear semigroups of operators ; 10. Unbounded self-adjoint operators and quadratic forms ; 11. Product formulas with applications to the Feynman integral ; 12. The Feynman-Kac formula ; 13. Analytic-in-time or mass operator-valued Feynman integrals ; 14. Feynman's operational calculus for noncommuting operators: An introduction ; 15. Generalised Dyson series, the Feynman integral and Feynman's operational calculus ; 16. Stability results ; 17. The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus ; 18. Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus ; 19. Feynman's operational calculus and evolution equations ; 20. Further work on or related to the Feynman integral ; References ; Index of symbols ; Author index ; Subject index