Discretized and covariant path integrals for stochastic processes - CNRS - Centre national de la recherche scientifique Access content directly
Preprints, Working Papers, ... Year : 2022

Discretized and covariant path integrals for stochastic processes


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.
Fichier principal
Vignette du fichier
2211.09470.pdf (1.28 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03865795 , version 1 (22-11-2022)



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



Gmail Facebook X LinkedIn More