A Dynamical Yukawa${}_2$ Model

Abstract

We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the Yukawa${}_2$ Euclidean field theory with a self-interacting boson. Our regularised dynamic is still singular but avoids non-local divergences, allowing us to use a version of the Da Prato--Debussche argument. This model is a test case for a non-commutative probability framework for formulating the kind of singular SPDEs arising in the stochastic quantisation of field theories mixing both bosons and fermions.

Added an argument using the Araki-Wyss representation to define a stronger non-commutative L^2 topology