The Feynman Integral and Feynman's Operational Calculus

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