Can the Lorenz-gauge potentials be considered physical quantities?

TL;DR

This paper argues that Lorenz-gauge potentials can be considered physical quantities because they satisfy causality, propagate at light speed, and can be expressed in a covariant form, linking them directly to observable fields.

Contribution

It introduces new expressions for Lorenz-gauge potentials in terms of electric and magnetic fields at retarded times, supporting their physical interpretation.

Findings

Potentials satisfy causality and propagate at light speed.

Potentials can be written in a covariant form.

Potentials can be regarded as causal effects of observed fields.

Abstract

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenz-gauge potentials at the present time in terms of electric and magnetic fields at the retarded time. These expressions provide a third result in favor of a physical interpretation of the Lorenz-gauge potentials: (iii) they can be regarded as causal effects of the observed electric and magnetic fields.