Commuting Clifford actions
Mathematical Physics
2024-10-29 v2 High Energy Physics - Theory
math.MP
Quantum Algebra
Abstract
It shown that if a vector space carries commuting actions of two Clifford algebras, then the quadratic monomials using generators from either Clifford algebra determine a spinor representation of an orthogonal Lie algebra. Examples of this construction have applications to high energy physics, particularly to the standard model and unification. It is shown how to use Clifford data to construct spectral triples for the Pati-Salam model that admit an action of Spin(10).
Cite
@article{arxiv.2405.08716,
title = {Commuting Clifford actions},
author = {John W. Barrett},
journal= {arXiv preprint arXiv:2405.08716},
year = {2024}
}
Comments
11 pages. v2: More explanation of the spectral triples. Other minor improvements