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A stochastic analysis of subcritical Euclidean fermionic field theories

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arxiv 2210.15047 v2 pith:2VYBPRA7 submitted 2022-10-26 math.PR math-phmath.MP

Francesco C. De Vecchi , Luca Fresta , Massimiliano Gubinelli This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords stochasticanalysisequationeuclideanfermionicfieldgrassmannsubcritical
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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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    A scale-by-scale flow equation with suitably chosen counterterms constructs renormalized solutions of fractional elliptic Phi^4 SPDEs throughout the subcritical regime.

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