Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Spectral Geometry for Causal Sets   We show that the Feynman propagator (or the d'Alembertian) of a causal set
contains the complete information about the causal set. Intuitively, this is
because the Feynman propagator, being a correlator that decays with distance,
provides a measure for the invariant distance between pairs of events. Further,
we show that even the spectra alone (of the self-adjoint and anti-self-adjoint
parts) of the propagator(s) and d'Alembertian already carry large amounts of
geometric information about their causal set. This geometric information is
basis independent and also gauge invariant in the sense that it is relabeling
invariant (which is analogue to diffeomorphism invariance). We provide
numerical evidence that the associated spectral distance between causal sets
can serve as a measure for the geometric similarity between causal sets.

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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an