An example of path integral reduction for a simple symmetric mechanical system on a product manifold

A path integral reduction procedure in Wiener-type path integrals, based on the approach developed in arXiv:1912.13124, is applied to a simple invariant mechanical system defined on a product manifold with a given free, proper and isometric action of the group SO(2). The Jacobian of the path integral reduction and the integral relation between the path integrals representing the fundamental solutions of the parabolic equations on initial and reduced manifolds are obtained.