Abstract
A nonperturbative QED is presented which is free of the divergences of perturbative QED. The theory comprises two equations of motion (EOM’s) for a relativistic electron which are mutually coupled by gauge-invariant self-electromagnetic interaction terms calculated from Maxwell’s equations. The first is Dirac’s equation itself, which Dirac required to be compatible with the material equation of continuity and which accounts for the electron’s rest-mass energy and spin-1/2 nature. The second is an EOM with Dirac form for a mass-0, spin-1/2 particle which I require to be compatible with the electromagnetic equation of continuity and which accounts for the electron’s charge and electromagnetic self energy such that the combined equations account for the electron’s rest-mass energy, spin, charge, and self energy and may therefore be regarded as a complete relativistic-electron theory. Due to the transverse nature of Maxwell’s equations the second EOM actually comprises two EOM’s: an EOM with magnetic-field interaction (MFEOM) accounting for radiative contributions to atomic structure and an EOM with electric-field interaction (EFEOM) investigated in this paper. The use of all three EOM’s together may be considered to describe radiation-dressed states of matter as opposed to radiation-bare states of matter as described by Dirac’s or Schroedinger’s equation alone. I argue that the EFEOM is physically appropriate for a neutrino for large separations of the two particles and is possibly associated with the electroweak force. On the other hand I show that for small interparticle separations the EFEOM shows binding on a GeV energy and Fermi-unit length scale such that one bare electron and two neutrinos with net spin-1 are possibly related to the muon or “heavy” electron. A model is constructed for muon structure and decay.
Highlights
Nonperturbative QED is normally associated with the coupled Dirac-Maxwell equations
On the other hand I show that for small interparticle separations the EFEOM shows binding on a GeV energy and Fermi-unit length scale such that one bare electron and two neutrinos with net spin-1 are possibly related to the muon or “heavy” electron
Future work should focus on the exact solution and investigate whether the Motion for the Electron’s Material Nature (MEOM)-REOM solution can accurately describe the muon, which is a “heavy electron” which decays into an electron and two neutrinos
Summary
Nonperturbative QED is normally associated with the coupled Dirac-Maxwell equations This approach, in which the electron’s self energy is assumed to arise from the classical Maxwell field whose source is the electron’s current calculated from Schroedinger’s or Dirac’s equation, was first investigated by Edwin Jaynes and co-workers (neoclassical radiation theory) over fifty years ago and by Assim Barut and co-workers over forty years ago (self-field quantum electrodynamics). These theories have been severely criticized by workers who use the quantized radiation field and the renormalization methodology proposed by Bethe in the late nineteen forties to calculate the Lamb shift and other radiative corrections to atomic structure. It is possible to criticize QED, notwithstanding its success in practical calculations following renormalization, on the basis that theory must be augmented by physical argument and ad hoc mathematical procedures to obtain agreement with experiment but that its pioneers failed to confront Lamb’s experiments in the first place as revolutionary for the www.ccsenet.org/apr
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