Okubo Algebra: a new approach to Quantum Chromodynamics?

Abstract: This talk discusses the possible relevance of the Okubonions (i.e. the real Okubo algebra) in quantum chromodynamics (QCD). We start and present the Okubonions within the 8-dimensional real division composition algebras, and then discuss their realization as the traceless cubic simple Jordan algebra over the complex numbers, endowed with a suitable deformation of the Michel-Radicati product. The Okubonions lack a unit element and exhibit the unique feature of sitting in the adjoint representation of their automorphism group SU(3); in this respect, they are fundamentally different from the better-known Octonions. While these latter may represent quarks (and singlets of the QCD SU(3) color gauge group), the Okubonions are conjectured to represent the gluons, i.e. the gauge bosons of the colour group. However, it is remarked that the SU(3) groups pertaining to Okubonions and Octonions are distinct and inequivalent subgroups of Spin(8) that share no common SU(2) subgroup. Main reference : arXiv:2309.17435 [hep-th]

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar