## Concerning the Dirac γ-Matrices Under a Lorentz Transformation of the Dirac Equation

**Authors:** Golden Gadzirayi Nyambuya

We embolden the idea that the Dirac 4 × 4 γ-matrices are four-vectors where the space components (γ i) represent spin and the forth component (γ 0) should likewise represent the time component of spin in the usual four-vector formalism of the Special Theory of Relativity. With the γ-matrices as four-vectors, it is seen that the Dirac equation admits two kinds of wavefunctions – (1) the usual four component Dirac bispinor ψ and (2) a scalar four component bispinor φ. Realizing this, and knowing forehand of the existing mystery as to why Leptons and Neutrinos come in pairs, we seize the moment and make the suggestion that the pair (ψ, φ) can be used as a starting point to explain mystery of why in their three generations [(e ± , ν e), (µ ± , ν µ), (τ ± , ν τ)], Leptons and Neutrinos come in doublets. In this suggestion, the scalar-bispinor φ can be thought of as the Neutrino while the usual Dirac bispinor ψ can be thought of as the Lepton.

**Comments:** 7 Pages.

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### Submission history

[v1] 2018-01-03 05:40:37

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