Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Infinitesimal Generators and Feynman-Kac Integrals of Adelic
  Diffusion   For each prime $p$, a Vladimirov operator with a positive exponent specifies
a $p$-adic diffusion equation and a measure on the Skorokhod space of $p$-adic
paths. The product, $P$, of these measures with fixed exponent is a probability
measure on the product of the $p$-adic path spaces. The adelic paths have full
measure if and only if the sum, $\sigma$, of the diffusion constants is finite.
Finiteness of $\sigma$ implies that there is an adelic Vladimirov operator,
$\Delta_{\mathbb A}$, and an associated diffusion equation whose fundamental
solution gives rise to the measure induced by $P$ on an adelic Skorokhod space.
For a wide class of potentials, the dynamical semigroups associated to adelic
Schr\"{o}dinger operators with free part $\Delta_{\mathbb A}$ have path
integral representations.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat