Fermion unification model based on the intrinsic SU(8) symmetry of a generalized Dirac equation

• Main Authors: Eckart eMarsch, Yasuhito eNarita
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2015-10-01
• Series: Frontiers in Physics
• Subjects: standard model; Generalized Dirac equation; elementary particle physics; Fermion unification; SU(8) symmetry group
• Online Access: http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00082/full

A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1) and the SU(3) groups, corresponding to quantum electrodynamics (QED based on electric charge) and chromodynamics (QCD based on colour charge). In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac) representations of the Dirac equation. This yields the SU(2) symmetry of the weak interaction, which can be married to U(1) to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8), which can accommodate and unify the observed eight basic stable fermions.