Stochastic quantisation is a stochastic analysis adapted to the multidimensional and distributional fields, in particular those arising in the Euclidean formulation of quantum field theory. In order to see this idea in action
I will give a sketch of a novel proof of the existence of the fractional Φ^4 Euclidean quantum field theory on the three dimensional Euclidean space and 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.
Joint work with Paolo Rinaldi (Bonn).