A stochastic analysis of subcritical Euclidean fermionic field theories

Francesco C. De Vecchi, Luca Fresta and Massimiliano Gubinelli

First issued 26 October 2022 · PDF · HTML

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.

Versions

1. Version 2 (arXiv v2) current
   20 June 2024
   arXiv comments: The errors in some proofs have been corrected and some typos have been fixed. Accepted for publication in Annals of Probability
   PDF · TeXmacs source · files and digests · arXiv:2210.15047
2. Version 1 (arXiv v1)
   26 October 2022
   arXiv comments: 48 pages
   PDF · TeXmacs source · files and digests · arXiv:2210.15047

Cite

Francesco C. De Vecchi, Luca Fresta and Massimiliano Gubinelli. A stochastic analysis of subcritical Euclidean fermionic field theories. Papers of Massimiliano Gubinelli, 2022, version 2. https://mgubi.org/papers/paper/fermionic-field-theories/

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