Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative geometry and stochastic processes   The recent analysis on noncommutative geometry, showing quantization of the
volume for the Riemannian manifold entering the geometry, can support a view of
quantum mechanics as arising by a stochastic process on it. A class of
stochastic processes can be devised, arising as fractional powers of an
ordinary Wiener process, that reproduce in a proper way a stochastic process on
a noncommutative geometry. These processes are characterized by producing
complex values and so, the corresponding Fokker-Planck equation resembles the
Schroedinger equation. Indeed, by a direct numerical check, one can recover the
kernel of the Schroedinger equation starting by an ordinary Brownian motion.
This class of stochastic processes needs a Clifford algebra to exist. In four
dimensions, the full set of Dirac matrices is needed and the corresponding
stochastic process in a noncommutative geometry is easily recovered as is the
Dirac equation in the Klein-Gordon form being it the Fokker--Planck equation of
the process.

37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th