On infinitesimal generators and Feynman–Kac integrals of adelic diffusion

For each prime p, a Vladimirov operator with positive exponent specifies p-adic diffusion equation and measure on the Skorokhod space of paths. The product, P, these measures fixed is probability product path spaces. adelic paths have full if only sum, σ, constants finite. Finiteness σ implies that there an operator, ΔA, associated whose fundamental solution gives rise to induced by P space. wide class potentials, dynamical semigroups Schrödinger operators free part ΔA integral representations.