Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Mechanics in General Relativity   Having started with the general formulation of the quantum theory of the real
scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the
general--covariant quasinonrelativistic quantum mechanics of a point-like
spinless particle in $ V_{1,3} $ is constructed. To this end, for any normal
geodesic 1+3--foliation of $ V_{1,3} $, a space $\Phi^-$ of asymptotic in
$c^{-1}$ solutions of the field equation is specified, which can be mapped to a
space $\Psi$ of solutions of a Schr\"odinger equation with an (asymptotically)
Hermitean hamiltonian and the Born probabilistic interpretation of the vectors
of $\Psi$. The basic operators of the momentum and the spatial position of the
particle acting in $\Psi$ generated by the corresponding observables of QFT
include relativistic corrections, and therefore differ generally from those
which follow for the geodesic motion in $ V_{1,3} $ from the canonical
postulates of quantization. In particular, the operators of coordinates do not
commute as well as the operators of the conjugate momenta, except the cases of
Cartesian coordinates in the Minkowski space--time or of the exact
nonrelativistic limit $(c^{-1} = 0)$. This approach provides QFT in the general
$ V_{1,3} $ in the Fock representation with a particle interpretation based on
the Born interpretation of wave functions.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys