Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity   We study the phase space structure and the quantization of a pointlike
particle in 2+1 dimensional gravity. By adding boundary terms to the first
order Einstein Hilbert action, and removing all redundant gauge degrees of
freedom, we arrive at a reduced action for a gravitating particle in 2+1
dimensions, which is invariant under Lorentz transformations and a group of
generalized translations. The momentum space of the particle turns out to be
the group manifold SL(2). Its position coordinates have non-vanishing Poisson
brackets, resulting in a non-commutative quantum spacetime. We use the
representation theory of SL(2) to investigate its structure. We find a
discretization of time, and some semi-discrete structure of space. An
uncertainty relation forbids a fully localized particle. The quantum dynamics
is described by a discretized Klein Gordon equation.

23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph