论文标题
关于机械系统的路径积分还原的几何表示，在歧管上给出的对称性的机械系统是主纤维束的总空间和矢量空间的总空间的产物
On the geometric representation of the path integral reduction Jacobian for a mechanical system with symmetry given on a manifold that is a product of the total space of the principal fiber bundle and the vector space
论文作者
论文摘要
对于由先前考虑的机械系统路径积分积分中的路径积分还原的问题引起的，具有对称性的对称性，描述了两个相互作用的标量粒子在歧管上的运动，这是光滑的紧凑型二级利马尼亚歧管的产物，并获得了有限维矢量空间，几何形式代表了几何形式。该表示从定义的原始歧管的标量曲率的公式遵循，并具有紧凑的半密度谎言组的自由等距平滑作用。该公式的推导是使用适应的坐标进行的，可以在研究中与该问题相关的主纤维束中确定。这些坐标类似于与标量场相互作用的Yang-Mills字段量化标准方法中使用的坐标。
For the Jacobian resulting from the previously considered problem of the path integral reduction in Wiener path integrals for a mechanical system with symmetry describing the motion of two interacting scalar particles on a manifold that is the product of a smooth compact finite-dimensional Riemannian manifold and a finite-dimensional vector space, a geometric representation is obtained. This representation follows from the formula for the scalar curvature of the original manifold endowed by definition with a free isometric smooth action of a compact semisimple Lie group. The derivation of this formula is performed using adapted coordinates, which can be determined in the principal fiber bundle associated with the problem under the study. These coordinates are similar to those used in the standard approach to quantization of Yang-Mills fields interacting with scalar fields.
