A Geometrical Model of Lepton Decay Based on Time Quantization

The unphysical runaway solutions of the Lorentz-Dirac equation are reanalyzed using the local Fermi-Walker rest frames of particles. We show that the radiation reaction term can be removed by a quantization of time ansatz. The result is that the runaway solutions for the free electron can be eliminated, and the runaway solutions for particles with masses greater than the electron can be reinterpreted as relating to particle decay processes. We elevate the coupling constant τ that appears in the Lorentz-Dirac equation to a classical parameter alongside the parameters mass m and charge q, and then geometrize the theory by introducing an SO(1, 2) geometry on the classical parameter space of triples (τ,m, q). For processes with ∆q = 0 we show that the eigenstates of the SO(1, 2) parameter space metric describe massive leptons and their corresponding neutrinos. We present a toy dynamical model that predicts masses close to the experimental masses of the tauon, the pion and the muon. When compared with the standard electroweak model we find that the electroweak coupling constants g l are defined by g l = τH τ l where τH and τl are the new time parameters of the Higgs particle and lepton l, respectively.