Three arguable and interrelated concepts: point particle singularity, asymmetric action of EM on quantum wave functions, and the Left out restricted Lorentz gauge from U(1)

Abstract

We address three issues. i. The point particle assumption, inherent to non-quantum physics, is singular and entails divergent fields and integrals. ii. In quantum physics EM plays an asymmetric roll. It acts on quantum wave fields (wave functions) but the wave fields do not react back. We suggest to promote the one sided action of EM on quantum fields into a mutual action-reaction partnership. By so doing, the quantum wave shares its analyticity with the EM field and removes the later's singularities and divergences. iii) The conventional U(1) symmetry leaves quantum dynamics invariant under a 'general' Lorentz gauge and impose the standard minimal coupling of the quantum wave to the Em 4-vector potential. One, however, has the option to ask for in-variance under the 'restricted' Lorentz gauge. This in turn invites in a coupling to derivatives of the vector potential in addition to the minimal coupling and, so to say, enlarges the U(1) symmetry. We find that the electron exhibits distributed charge- and current- densities. The enlarged symmetry is expected to bring in its own constant of motion. Indeed it does. The anomalous g-factor of the so designed electron emerges, up to order ({\alpha}/{\pi})^2 as the new constant of motion but, without invoking the QED formalism.