A Dynamical Yukawa$_{2}$ Model
Probability
2024-03-07 v2 Mathematical Physics
math.MP
Operator Algebras
Abstract
We prove local (in space and time) well-posedness for a mildly regularised version of the stochastic quantisation of the Yukawa 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.
Cite
@article{arxiv.2305.07388,
title = {A Dynamical Yukawa$_{2}$ Model},
author = {Ajay Chandra and Martin Hairer and Martin Peev},
journal= {arXiv preprint arXiv:2305.07388},
year = {2024}
}
Comments
Added an argument using the Araki-Wyss representation to define a stronger non-commutative L^2 topology