English

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 Yukawa2_{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.

Keywords

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

R2 v1 2026-06-28T10:32:50.365Z