Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical analysis and symmetry reduction I. Equivariant Weyl law
  for invariant Schr\"odinger operators on compact manifolds   We study the spectral properties of Schr\"odinger operators on a compact
connected Riemannian manifold $M$ without boundary in case that the underlying
Hamiltonian system possesses certain symmetries. More precisely, if $M$ carries
an isometric and effective action of a compact connected Lie group $G$, we
prove a generalized equivariant version of the semiclassical Weyl law with an
estimate for the remainder, using a semiclassical functional calculus for
$h$-dependent functions and relying on recent results on singular equivariant
asymptotics. These results will be used to derive an equivariant quantum
ergodicity theorem in Part II of this work. When $G$ is trivial, one recovers
the classical results.

20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th