Affiliation:
1. Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
Abstract
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.
Funder
Science and Technology Facilities Council
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
1 articles.
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