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

TL;DR

This paper constructs a fractional $\

Contribution

It introduces a novel parabolic stochastic quantisation method for the fractional $\

Findings

Constructs the fractional $\

Establishes invariance and positivity properties of the measure

Provides coercive estimates for the associated SPDE

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.