Abstract
In this paper, the notion of spin helicity is generalized into threefold spin helicity. It appears to be a useful means to extend the standard Dirac equation to describe coloured fermions. The threefold generalization of helicity is derived from the mass shell condition, spin, and kinetic helicity in a natural way. It is found that the three different types of helicities are associated with the rotation degrees of freedom in 3-D coordinate space. Moreover, threefold helicity can by unitary transformation be connected with the empirical SU(3) colour symmetry of the quarks, and thus be brought into the mathematical form of the SU(3) Yang–Mills gauge theory of the standard model. This offers an alternative picture of the physical origin of quark symmetry in compliance with the Coleman–Mandula theorem.
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