### Nonperturbative QED: Muon Structure and Decay

#### 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.

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