The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group. The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory. The integral relation between the kernels of the original and reduced semigroup are obtained.
On the geometric representation of the path integral reduction Jacobian in the path integral for interacting systems: The case of dependent coordinates in the description of reduced motion on the orbit space
本文找到了 Wiener 型路径积分中路径积分约化 Jacobi 行列式的几何表示，用于描述紧致半单 Lie 群自由等距作用下两相互作用标量粒子的运动，基于主纤维丛全空间的标量曲率公式，在水平提升基中完成了 Christoffel 符号与曲率计算。
Reply to comment on calculation of two-center nuclear attraction integrals over integer and noninteger n-Slater-type orbitals in nonlined-up coordinate systems
