论文标题
动态系统的路径积分的非零动量水平降低，其在产品歧管上给出的对称性，由主纤维束的总空间和矢量空间组成
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
论文作者
论文摘要
机械系统的Wiener路径积分中非零动量水平降低的情况，其对称性描述了与给定动作的Riemannian乘积歧管上相互作用的两个标量颗粒的运动，也考虑了紧凑的半精密谎言组。原始产物歧管由矢量空间和平滑的紧凑型二维riemannian歧管组成，由于该组的作用，可以将其视为主要纤维束的总空间。代表主要纤维束总空间（原始的Riemannian乘积歧管）和相应的后向Kolmogorov方程式的向后kolmogorov方程的基本解的路径积分之间的整体关系。
The case of non-zero momentum level reduction in Wiener path integrals for a mechanical system with symmetry describing the motion of two scalar particles with interaction on a Riemannian product manifold with the given action a compact semisimple Lie group is considered. The original product manifold consists of the vector space and a smooth compact finite-dimensional Riemannian manifold, which, due to the action of the group, can be regarded as the total space of the principal fiber bundle. The integral relation between the path integrals representing the fundamental solutions of the backward Kolmogorov equation defined on the total space of the principal fiber bundle (the original Riemannian product manifold) and the corresponding backward Kolmogorov equation gion the space of the sections of the associated covector bundle is obtained.
