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arXiv · 2210.15047

A stochastic analysis of subcritical Euclidean fermionic field theories

Francesco C. De Vecchi·Luca Fresta·Massimiliano Gubinelli
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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.

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Francesco C. De Vecchi, Luca Fresta, Massimiliano Gubinelli. 2022-10-26. A stochastic analysis of subcritical Euclidean fermionic field theories. https://arxiv.org/abs/2210.15047

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