Feynman-Kac formula for Lévy processes and semiclassical (Euclidean) momentum representation

We prove a version of the Feynman-Kac formula for Lévy processes and integro-differential operators, with application to the momentum representation of suitable quantum (Euclidean) systems whose Hamiltonians involve Lévytype potentials. Large deviation techniques are used to obtain the limiting behavior of the systems as the Planck constant approaches zero. It turns out that the limiting behavior coincides with fresh aspects of the semiclassical limit of (Euclidean) quantum mechanics. Non-trivial examples of Lévy processes are considered as illustrations and precise asymptotics are given for the terms in both configuration and momentum representations.