• 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

" I would recommend this book to serious students of the subject." Physics Today

• 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

" I would recommend this book to serious students of the subject." Physics Today

• 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

" I would recommend this book to serious students of the subject." Physics Today