Feynman formulas for averaging of semigroups, generating by the operators of Schrödinger type

Abstract:

The averaging procedure of one-parametric semigroups, based on Chernoff equivalence for operator-functions is constructed. The initial problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of freedom motion. It is established, that in these examples the quantization can be treated as averaging of random translation operators in classical coordinate space.