A stochastic analysis of subcritical Euclidean fermionic field theories
Probability
2024-06-21 v2 Mathematical Physics
math.MP
Abstract
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is inspired by the so-called continuous renormalisation group, but avoids the technical difficulties encountered in the direct study of the flow equation for the effective potentials. As an application, we construct a family of weakly coupled subcritical Euclidean fermionic field theories and prove exponential decay of correlations.
Keywords
Cite
@article{arxiv.2210.15047,
title = {A stochastic analysis of subcritical Euclidean fermionic field theories},
author = {Francesco C. De Vecchi and Luca Fresta and Massimiliano Gubinelli},
journal= {arXiv preprint arXiv:2210.15047},
year = {2024}
}
Comments
The errors in some proofs have been corrected and some typos have been fixed. Accepted for publication in Annals of Probability