Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Point particles in 2+1 dimensions: general relativity and loop gravity
  descriptions   We develop a Hamiltonian description of point particles in (2+1)-dimensions
using connection and frame-field variables for general relativity. The topology
of each spatial hypersurface is that of a punctured two-sphere with particles
residing at the punctures. We describe this topology with a CW complex (a
collection of two-cells glued together along edges), and use this to fix a
gauge and reduce the Hamiltonian. The equations of motion for the fields
describe a dynamical triangulation where each vertex moves according to the
equation of motion for a free relativistic particle. The evolution is
continuous except for when triangles collapse (i.e. the edges become parallel)
causing discrete, topological changes in the underlying CW complex.
  We then introduce the loop gravity phase space parameterized by holonomy-flux
variables on a graph (a network of one-dimensional links). By embedding a graph
within the CW complex, we find a description of this system in terms of loop
variables. The resulting equations of motion describe the same dynamical
triangulation as the connection and frame-field variables. In this framework,
the collapse of a triangle causes a discrete change in the underlying graph,
giving a concrete realization of the graph-changing moves that many expect to
feature in full loop quantum gravity. The main result is a dynamical model of
loop gravity which agrees with general relativity and is well-suited for
quantization using existing methods.

27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex