Parabolic stochastic quantisation of the fractional $\Phi^4_3$ model in the full subcritical regime

Paweł Duch; Massimiliano Gubinelli; Paolo Rinaldi

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arXiv · 2303.18112

Parabolic stochastic quantisation of the fractional $\Phi^4_3$ model in the full subcritical regime

Paweł Duch·Massimiliano Gubinelli·Paolo Rinaldi

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Abstract

We present a construction of the fractional $\Phi^4$ Euclidean quantum field theory on $\mathbb{R}^3$ in the full subcritical regime via parabolic stochastic quantisation. Our approach is based on the use of a truncated flow equation for the effective description of the model at sufficiently small scales and on coercive estimates for the non-linear stochastic partial differential equation describing the interacting field. The measure is invariant under translations, reflection positive and has quartic exponential tails.

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Paweł Duch, Massimiliano Gubinelli, Paolo Rinaldi. 2023-03-31. Parabolic stochastic quantisation of the fractional $\Phi^4_3$ model in the full subcritical regime. https://arxiv.org/abs/2303.18112

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