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Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions (2305.12017v2)

Published 19 May 2023 in math-ph, math.MP, math.OA, and math.PR

Abstract: We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic quantization (SQ). In particular we consider the elliptic stochastic quantization of the H{\o}egh--Krohn (or $\exp (\alpha \phi)_2$) EQFT in two dimensions. The first method is based on a path-wise coupling argument and PDE apriori estimates while the second on estimates of the Malliavin derivative of the solution to the SQ equation.

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