The Classical Equations of Motion of Quantized Gauge Theories, Part 2: Electromagnetism

TL;DR

This paper demonstrates that quantized electromagnetism allows classical electric field states that violate Gauss's law, potentially influencing charged particle dynamics through a gauge-invariant, Schrödinger-evolved 'shadow' charge density.

Contribution

It reveals the existence of gauge-invariant electric field states violating Gauss's law in quantum electromagnetism, expanding the understanding of classical dynamics in gauge theories.

Findings

Existence of gauge-invariant electric field states violating Gauss's law.

These states can be described by the Schrödinger equation.

Shadow charge density may influence particle dynamics.

Abstract

In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the existence of classical electric field states that do not obey Gauss's law. These states are gauge invariant and their time evolution can be consistently described using the Schr\"{o}dinger equation. The time evolution of these states is such that at the classical level, the full set of Maxwell's equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, static ``shadow'' charge density with no internal degrees of freedom. This density could affect the dynamics of charged particles in our universe and it may thus be of observational interest.