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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).

Keywords

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

R2 v1 2026-06-28T16:27:10.540Z