Comment on gauge choices and physical variables in QED

TL;DR

This paper analyzes different gauge choices in QED, showing that the Coulomb gauge is most convenient but others like $A_3=0$ are also viable, and clarifies misconceptions about overconstraint issues.

Contribution

It compares gauge choices in QED, demonstrating the convenience of Coulomb gauge and clarifying the status of the $A_3=0$ gauge regarding constraints.

Findings

Coulomb gauge leads to local action in path integrals.

$A_3=0$ gauge is not overconstrained as previously claimed.

Different gauge choices are viable for defining physical variables in QED.

Abstract

We consider possible definitions of physical variables in QED. We demonstrate that the condition $\partial_i A_i$$=0$ is the most convenient one because it leads to path integral over physical components with local action. However, other choices, as $A_3=0$, are also possible. The standard expression for configuration space path integral in $A_3=0$ gauge is obtained starting with reduced phase space formulation. Contrary to the claims of the paper [M.Lavelle and D.McMullan,Phys. Lett. B316 (1993)172] the $A_3=0$ gauge is not overconstrained.