Stochastic quantization of an Abelian gauge theory
Probability
2019-06-03 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the Langevin dynamics of a U(1) lattice gauge theory on the torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. This also yields convergence of some gauge invariant observables on a short time interval. We fix gauge via a DeTurck trick, and prove a version of Ward identity which results in cancellation of renormalization constants that would otherwise break gauge symmetry. The proof relies on a discrete version of the theory of regularity structures.
Cite
@article{arxiv.1801.04596,
title = {Stochastic quantization of an Abelian gauge theory},
author = {Hao Shen},
journal= {arXiv preprint arXiv:1801.04596},
year = {2019}
}
Comments
67 pages, rewrote and improved some of the proofs