Local charge conservation law as a source of gauge condition in quantum electrodynamics

TL;DR

This paper proposes a novel formulation of quantum electrodynamics where local charge conservation determines the gauge condition, integrating charge density dynamics and modified asymptotic states into the quantum framework.

Contribution

It introduces a new approach where charge conservation law acts as the gauge condition source, linking charge distribution dynamics with gauge fixing in quantum electrodynamics.

Findings

Charge conservation law can serve as a gauge condition in QED.

Charge distribution dynamics are incorporated into the quantum theory.

Modified asymptotic states involve charged wave packets instead of free particles.

Abstract

A formulation of quantum electrodynamics is proposed, in which the local law of conservation of electric charge serves as the source of the gauge condition. The equations of motion of the gauge variable and the density of the charge distribution in space following from this law are introduced into the quantum theory as additional conditions. Along with fixing the gauge, the interaction of charges in the modified quantum theory is described by the dynamics of the charge distribution density. The asymptotic states of free particles at spatial infinity are replaced by the initial and final states of the electromagnetic system in the form of charged wave packets.