Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path Integral Quantisation of Finite Noncommutative Geometries   We present a path integral formalism for quantising gravity in the form of
the spectral action. Our basic principle is to sum over all Dirac operators.
The approach is demonstrated on two simple finite noncommutative geometries:
the two-point space, and the matrix geometry M_2(C). On the first, the graviton
is described by a Higgs field, and on the second, it is described by a gauge
field. We start with the partition function and calculate the propagator and
Greens functions for the gravitons. The expectation values of distances are
evaluated, and we discover that distances shrink with increasing graviton
excitations. We find that adding fermions reduces the effects of the
gravitational field. A comparison is also made with Rovelli's canonical
quantisation approach, and with his idea of spectral path integrals. We include
a brief discussion on the quantisation of a Riemannian manifold.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat