Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path Integrals on Riemannian Manifolds with Symmetry and Induced Gauge
  Structure   We formulate path integrals on any Riemannian manifold which admits the
action of a compact Lie group by isometric transformations. We consider a path
integral on a Riemannian manifold M on which a Lie group G acts isometrically.
Then we show that the path integral on M is reduced to a family of path
integrals on a quotient space Q=M/G and that the reduced path integrals are
completely classified by irreducible unitary representations of G. It is not
necessary to assume that the action of G on M is either free or transitive.
Hence our formulation is applicable to a wide class of manifolds, which
includes inhomogeneous spaces, and it covers all the inequivalent
quantizations. To describe the path integral on inhomogeneous space,
stratification geometry, which is a generalization of the concept of principal
fiber bundle, is necessarily introduced. Using it we show that the path
integral is expressed as a product of three factors; the rotational energy
amplitude, the vibrational energy amplitude, and the holonomy factor. When a
singular point arises in $ Q $, we determine the boundary condition of the path
integral kernel for a path which runs through the singularity.

26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas