Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
Abstract
Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of 7 unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is tighter and more explanatory than the traditional one based on effective field theory.
Keywords
Cite
@article{arxiv.1401.5083,
title = {Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics},
author = {Latham Boyle and Shane Farnsworth},
journal= {arXiv preprint arXiv:1401.5083},
year = {2015}
}
Comments
5 pages, no figures, matches published version