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Preprints, Working Papers, ... Year : 2022

Discretized and covariant path integrals for stochastic processes

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Abstract

Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations - such as performing a change of the integration path - one would like to carry out in the light-hearted fashion that physicists enjoy. Similar issues arise in the field of stochastic calculus, which we review to prepare the ground for a proper construction of path integrals. At the level of path integration, and in arbitrary space dimension, we not only report on existing Riemannian geometry-based approaches that render path integrals amenable to the standard rules of calculus, but also bring forth new routes, based on a fully time-discretized approach, that achieve the same goal. We illustrate these various definitions of path integration on simple examples such as the diffusion of a particle on a sphere.
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hal-03865795 , version 1 (22-11-2022)

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Thibaut Arnoulx de Pirey, Leticia F. Cugliandolo, Vivien Lecomte, Frédéric van Wijland. Discretized and covariant path integrals for stochastic processes. 2022. ⟨hal-03865795⟩
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