Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic Continuation of Stochastic Mechanics   We study a (relativistic) Wiener process on a complexified
(pseudo-)Riemannian manifold. Using Nelson's stochastic quantization procedure,
we derive three equivalent descriptions for this problem. If the process has a
purely real quadratic variation, we obtain the one-sided Wiener process that is
encountered in the theory of Brownian motion. In this case, the result
coincides with the Feyman-Kac formula. On the other hand, for a purely
imaginary quadratic variation, we obtain the two-sided Wiener process that is
encountered in stochastic mechanics, which provides a stochastic description of
a quantum particle on a curved spacetime.

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The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga