nLab Feynman-Kac formula



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The Feynman–Kac formula expresses the integral kernel of the one-parameter semigroup generated by a Laplacian on a smooth manifold as the path integral of the parallel transport map associated to the given connection with respect to all paths of a given length connecting the two given points.


The original reference is

  • Mark Kac, On distributions of certain Wiener functionals, Transactions of the American Mathematical Society 65:1 (1949), 1–13. doi.

The case of smooth manifolds is treated in

  • James R. Norris, A complete differential formalism for stochastic calculus in manifolds, Séminaire de Probabilités XXVI, Lecture Notes in Mathematics (1992), 189–209. doi.

Last revised on June 20, 2022 at 20:04:28. See the history of this page for a list of all contributions to it.