Three Arguables: Point Particle Singularity, Asymmetry in EM and Quantum Waves, and the Left Out Restricted Lorentz Gauge from U(1)

We address three issues: (1) The point particle assumption inherent to non-quantum physics is singular and entails divergent fields and integrals. (2) In quantum physics electromagnetism (EM) plays an asymmetric roll. It acts on quantum wave functions (QW) but QW does not react back. We suggest to promote the one-sided action of EM on QW into a mutual action-reaction status. This enables QW to share its non-singular feature with EM and to remove the Coulomb singularity. (3) Quantum mechanics is U(1) symmetric. QW multiplied by an arbitrary phase factor and EM written in7 the same Lorentz gauge, leave both EM and QW invariant. The minimal coupling of QW to the EM 4-vector potential, \({{A}_{\mu }}\), is a consequence of this arbitrary gauge. Symmetry under the restricted Lorentz gauge, is left out. We propose to enlarge U(1) to accommodate the restricted Lorentz gauge as well. This in turn invites in a coupling of QW to the derivatives of the vector potential, \({{\partial }_{\nu }}{{A}_{\mu }}\), in addition to the minimal coupling. We find that (i) electron acquires a distributed charge, reminiscent of the QED-renormalized charge distributions; (ii) because of its spin, electron acquires a self induced magnetic moment with the same g-factor as in QED but without relying on QED.