Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path integrals and the essential self-adjointness of differential
  operators on noncompact manifolds   We consider Schr\"odinger operators on possibly noncompact Riemannian
manifolds, acting on sections in vector bundles, with locally square integrable
potentials whose negative part is in the underlying Kato class. Using path
integral methods, we prove that under geodesic completeness these differential
operators are essentially self-adjoint on the space of smooth functions with
compact support, and that the corresponding operator closures are semibounded
from below. These results apply to nonrelativistic Pauli-Dirac operators that
describe the energy of Hydrogen type atoms on Riemannian 3-manifolds.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an