Yang-Mills for probabilists
Abstract
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This article presents a formulation of some of the core aspects this problem as problems in probability theory. The presentation begins with an introduction to the basic setup of Euclidean Yang-Mills theories and lattice gauge theories. This is followed by a discussion of what is meant by a continuum limit of lattice gauge theories from the point of view of theoretical physicists. Some of the main issues are then posed as problems in probability. The article ends with a brief review of the mathematical literature.
Keywords
Cite
@article{arxiv.1803.01950,
title = {Yang-Mills for probabilists},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1803.01950},
year = {2018}
}
Comments
17 pages