Regularity structures and the dynamical $Φ^4_3$ model
Year: 2015
Type: preprint
Abstract: We give a concise overview of the theory of regularity structures as first exposed in [Hai14]. In order to allow to focus on the conceptual aspects of the theory, many proofs are omitted and statements are simplified. In order to provide both motivation and focus, we concentrate on the study of solutions to the stochastic quantisation equations for the Euclidean $Φ^4_3$ quantum field theory which can be obtained with the help of this theory. In particular, we sketch the proofs of how one can show that this model arises quite naturally as an idealised limiting object for several classes of smooth models.
Author: Hairer, Martin
Institution: University of Warwick
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Leverhulme Trust
OpenAlex ID: W4299150833