CrossRef Open Access 2022 3 sitasi

Analytic continuation of stochastic mechanics

Folkert Kuipers

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Abstrak

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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Folkert Kuipers

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Kuipers, F. (2022). Analytic continuation of stochastic mechanics. https://doi.org/10.1063/5.0073096

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Lihat di Sumber doi.org/10.1063/5.0073096

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Total Sitasi: 3×
Sumber Database: CrossRef
DOI: 10.1063/5.0073096
Akses: Open Access ✓