## Lepton Generation Problem, Some Properties and Implications of the Curved Spacetime Dirac Equation.

**Authors:** Golden Gadzirayi Nyambuya

This reading is a continuation of the earlier reading Nyambuya (2008); where three new Curved
Spacetime Dirac Equations have been derived mainly to try and account in a natural way for the observed
anomalous gyromagnetic ratio of fermions and the suggestions is that particles including the Electron, which
is thought to be a point particle, do have a finite spatial size and this is one of the reasons for the observed
anomalous gyromagnetic ratio. Combining the idea in Nyambuya (2008) which lead to the derivation of the
three new Curved Spacetime Dirac Equations, and the proposed Unified Field Theory (Nyambuya 2007), a
total of 12 equations each with 16 sub-components are generated thus leading to a total of 192 equations for
the Curved Spacetime Dirac Equation. Some symmetries of these equations are investigated, i.e., the Lorentz
symmetry, charge conjugation symmetry (C), time reversal symmetry (T), Space reversal (P) and a combination
of the C, P&T-symmetries. It is shown that these equations are Lorentz invariant, obey C-symmetry and that
some violate T and P-symmetry while others do not and that they all obey PT-symmetry. These symmetries
show (or modestly said - seem to suggest) that anti-particles have positive mass and energy but a negative
rest-mass and the opposite sign in electronic charge. Through the inspection of these symmetries, a suggestion
is (here) made to the effect that the rest-mass of a particle must be related to the electronic charge of that
particle thus leading us to a possible resolution of whether or not Neutrinos do have a none-zero rest-mass.
Additionally, we demonstrate that these equations have the potency to explain naturally the observed lepton
generation phenomena.

**Comments:** 12 pages, 1 figure, 5 tables, Submitted to the Apeiron Journal

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### Submission history

[v1] 18 Nov 2009

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