Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase space quantization, noncommutativity and the gravitational field   In this paper we study the structure of the phase space in noncommutative
geometry in the presence of a nontrivial frame. Our basic assumptions are that
the underlying space is a symplectic and parallelizable manifold. Furthermore,
we assume the validity of the Leibniz rule and the Jacobi identities. We
consider noncommutative spaces due to the quantization of the symplectic
structure and determine the momentum operators that guarantee a set of
canonical commutation relations, appropriately extended to include the
nontrivial frame. We stress the important role of left vs. right acting
operators and of symplectic duality. This enables us to write down the form of
the full phase space algebra on these noncommutative spaces, both in the
noncompact and in the compact case. We test our results against the class of 4D
and 6D symplectic nilmanifolds, thus presenting a large set of nontrivial
examples that realize the general formalism.

32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc