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The case of non-zero momentum level reduction in Wiener path integrals for amechanical system with symmetry describing the motion of two scalar particleswith interaction on a Riemannian product manifold with the given action acompact semisimple Lie group is considered. The original product manifoldconsists of the vector space and a smooth compact finite-dimensional Riemannianmanifold, which, due to the action of the group, can be regarded as the totalspace of the principal fiber bundle. The integral relation between the pathintegrals representing the fundamental solutions of the backward Kolmogorovequation defined on the total space of the principal fiber bundle (the originalRiemannian product manifold) and the corresponding backward Kolmogorov equationgion the space of the sections of the associated covector bundle is obtained.

Non-zero momentum level reduction in path integrals for dynamical  systems with symmetry given on a product manifold consisting of the total  space of the principal fiber bundle and a vector space