Feynman-Kac formula for 1st order perturbations of covariant Laplace-type operators

31.05.2021, 14:00  –  Zoom
Forschungsseminar Wahrscheinlichkeitstheorie

Batu Güneysu (UP)

It is a classical fact that one can represent the heat semigroup of a Schrödinger operator (that is, a perturbation of the Laplacian by a real-valued potential) as a path integral in terms of Brownian motion: this is the celebrated Feynman-Kac formula. The aim of this talk is to explain a non-selfadjoint variant of this result, where one allows arbitrary first order perturbations of a Bochner-Laplacian that acts on sections of a vector bundle over an arbitrary noncompact Riemannian manifold. In particular, one replaces self-adjoint heat semigroups by holomorphic semigroups. As an application in noncommutative geometry, we obtain an explicit path integral formula for the first degree part of the differential graded Chern character of an even dimensional Riemannian spin manifold. This is joint work with Sebastian Boldt (Leipzig).


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