Lepton Generation Problem, Some Properties and Implications of the Curved Spacetime Dirac Equation -- (II)

TL;DR

This paper extends the Curved Spacetime Dirac Equation framework to explore symmetries, particle properties, and lepton generation, proposing that particle rest-mass relates to electric charge and offering insights into neutrino mass.

Contribution

It introduces a comprehensive set of 192 Curved Spacetime Dirac Equations with symmetry analysis, linking particle mass to charge and explaining lepton generation phenomena.

Findings

Equations are Lorentz invariant and obey C and PT symmetries.

Some equations violate T and P symmetries, others do not.

The approach suggests a relation between particle rest-mass and electric charge.

Abstract

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 and 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.