The Electron and the Muon as Eigensolutions of the Quantum Electromechanics under the Green-Function δ (x2 + l2)

Abstract

Abstract Replacing the Green function of Maxwell's electrodynamics δ(x2) by δ(x2 + l2) we obtain a Hamiltonian with a finite number of degrees of freedom for the classical motion of a pointcharge in its own electromagnetic field. After quantization we obtain a mass spectrum if we assume that a nonelectrodynamic bare mass M exists. The spectral terms are S1/2 , P1/2; P3/2 , D3/2; D5/2 etc. (k = +1, -1; +2, -2; +3 ...). It is possible to fit the length l in the Green function and the mass M so that the mass ratio of the lowest terms becomes m (P1/2)/m(S1/2) = mμ/me . We then get: l =4,896 · 10-91 ħ/mp c, M = 15,32mp . Hence the deviation from Maxwell's electrodynamic is extremely small, but not zero, and heavy leptons should exist near m = | M | . Some further leptonic states exist with masses similar to that of the muon. All states, those of the electron and the muon excepted, are γ-instable (life time 10-17 sec. resp. 10-26 sec.).