Evolution semigroups generated by pseudo-differential operators are considered. These
operators are obtained by different (parameterized by a number τ) procedures of …

This note is devoted to Feynman formulas (ie, representations of semigroups by limits of n-
fold iterated integrals as n→∞) and their connections with phase space Feynman path …

A Feynman formula is a representation of a solution of an initial (or initial-boundary) value
problem for an evolution equation (or, equivalently, a representation of the semigroup …

A method to describe classical and quantum evolution systems is presented. The method is
based on the so-called Feynman formulae, ie on representations of solutions of evolution …

A Feynman formula is a representation of the semigroup, generated by an initial-boundary
value problem for some evolutionary equation, by a limit of integrals over Cartesian powers …

In the present paper, we find representations of a one-parameter semigroup generated by a
finite sum of iterated Laplace operators and an additive perturbation (the potential). Such …

One of the most challenging problems of modern physics is the connection between the
macroscopic and the microscopic world, that is between classical and quantum mechanics …

A simple general approach to the construction of measures on path space is developed. It is
used for the path integral representation of evolutionary equations including Feller …

The Feyrtman formula is a representation of either a Schrodinger semigroup elH or a
Schrodinger group ettH hy limits of superpositions of some multiple integrals, over Cartesian …

The Feynman path integral is known to be a powerful tool in different domains of physics. 1
At the same time, the mathematical theory underlying lots of (often formal) physical …