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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTime6 days ago

    Created:

    Idea

    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.

    References

    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.

    v1, current

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