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Physics with non-unital algebras? an invitation to the okubo algebra
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Resumo(s)
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 SUO, 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.
Descrição
Palavras-chave
Non-associative algebras Okubo algebra Quantum chromodynamics Representation theory Octonions Gauge theory
Contexto Educativo
Citação
Editora
IOP Publishing