Integer versions of Yang-Mills theory
Group Theory
2022-03-09 v3 High Energy Physics - Theory
Abstract
In a recent paper, 't Hooft asks for an integer version of Yang-Mills theory, in the belief that this is the way the universe really is at the Planck scale. Specifically, he asks for an integer version of the gauge group of the standard model. Such groups were completely classified more than 100 years ago, and here I detail the group theory and representation theory (and some of the physics) of the specific case that I believe answers 't Hooft's question.
Cite
@article{arxiv.2202.08263,
title = {Integer versions of Yang-Mills theory},
author = {R. A. Wilson},
journal= {arXiv preprint arXiv:2202.08263},
year = {2022}
}
Comments
v3: 20 pages; added sections on the equivalence principle, quantum gravity, and symmetry-breaking. v2: added sections on the derivation of effective field theories and the standard model from the proposed fundamental model