English

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

R2 v1 2026-06-24T09:41:30.642Z