Physics with non-unital algebras? An invitation to the Okubo algebra

This paper presents some preliminary discussion on the possible relevance of the Okubonions, i.e. the real Okubo algebra O , in quantum chromodynamics (QCD). The Okubo algebra lacks a unit element and sits in the adjoint representation of its automorphism group SU O , thus being fundamentally different from the better-known octonions O . While these latter may represent quarks (and color singlets), the Okubonions are conjectured to represent the gluons, i.e. the gauge bosons of the QCD SU ( 3 ) color symmetry. However, it is shown 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. The unusual properties of Okubonions may be related to peculiar QCD phenomena like asymptotic freedom and color confinement, though the actual mechanisms remain to be investigated.