Aharonov--Bohm effect, electrodynamics postulates, and Lorentz condition

TL;DR

This paper proposes that microscopic electrodynamics should be based on the d'Alembert equations for the electromagnetic potential, with the Lorentz condition valid only for averages, resolving issues related to the Aharonov-Bohm effect and field quantization.

Contribution

It introduces a framework where Maxwell equations apply only to averaged fields, explaining the Aharonov-Bohm effect and the nature of virtual photons within quantum electrodynamics.

Findings

Maxwell equations are valid only for averaged fields.

Microscopic electrodynamics is based on d'Alembert equations for potentials.

Longitudinal and scalar photons are formal constructs related to Coulomb interaction and Aharonov-Bohm effect.

Abstract

The problem of the relation between the Ahronov-Bohm effect and traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. We proceed from the idea that the Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics should be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorentz condition is valid only for the averages and provides the implementation of the Maxwell equations for averages. This concept eliminates the problem of electromagnetic field quantization and provides the correctness of all known results of quantum electrodynamics. Therefore, the "virtuality" of the longitudinal and scalar photons has a formal mathematical character, conditioned by the Maxwell equations for averaged fields. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.