Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path integral representation of the quantum evolution in dynamical
  systems with a symmetry for the non-zero momentum level reduction   For the case of reduction onto the non-zero momentum level, in the problem of
the path integral quantization of a scalar particle motion on a smooth compact
Riemannian manifold with the given free isometric action of the compact
semisimle Lie group, the path integral representation of the matrix Green's
function, which describes the quantum evolution of the reduced motion, has been
obtained. The integral relation between the path integrals representing the
fundamental solutions of the parabolic differential equation defined on the
total space of the principal fiber bundle and the linear parabolic system of
the differential equations on the space of the sections of the associated
covector bundle has been derived.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin