Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Quantum Physics and Noncommutative Geometry   Conventional discrete approximations of a manifold do not preserve its
nontrivial topological features. In this article we describe an approximation
scheme due to Sorkin which reproduces physically important aspects of manifold
topology with striking fidelity. The approximating topological spaces in this
scheme are partially ordered sets (posets). Now, in ordinary quantum physics on
a manifold $M$, continuous probability densities generate the commutative
C*-algebra $\cc(M)$ of continuous functions on $M$. It has a fundamental
physical significance, containing the information to reconstruct the topology
of $M$, and serving to specify the domains of observables like the Hamiltonian.
For a poset, the role of this algebra is assumed by a noncommutative C*-algebra
$\ca $. As noncommutative geometries are based on noncommutative C*-algebras,
we therefore have a remarkable connection between finite approximations to
quantum physics and noncommutative geometries. Various methods for doing
quantum physics using $\ca $ are explored. Particular attention is paid to
developing numerically viable approximation schemes which at the same time
preserve important topological features of continuum physics.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con