2022/04/03 by Thibaut Arnoulx de Pirey, Leticia F. Cugliandolo, Vivien Lecomte +1 · 4 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Electrodynamics and Casimir Effect #Cosmology and Gravitation Theories
paper · doi:10.1080/00018732.2023.2199229
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.