Physical Angular Momentum Separation for QED

TL;DR

This paper addresses the non-uniqueness of gauge-invariant angular momentum separation in QED, proposing a unique scheme for free QED based on Euclidean symmetry and extending ideas to interacting QED.

Contribution

It identifies a unique angular momentum separation scheme in free QED using Euclidean symmetry and proposes natural schemes for interacting QED via asymptotic fields.

Findings

Euclidean symmetry selects a unique angular momentum scheme in free QED.

Proposed natural angular momentum separation schemes for interacting QED.

Brief discussion on extending the framework to QCD.

Abstract

We study the non-uniqueness problem of the gauge-invariant angular momentum separation for the case of QED, which stems from the recent controversy concerning the proper definitions of the orbital angular momentum and spin operator of the individual parts of a gauge field system. For the free quantum electrodynamics without matter, we show that the basic requirement of Euclidean symmetry selects a unique physical angular momentum separation scheme from the multitude of the possible angular momentum separation schemes constructed using the various Gauge Invariant Extentions. Based on these results, we propose a set of natural angular momentum separation schemes for the case of interacting QED by invoking the formalism of asymptotic fields. Some perspectives on such a problem for the case of QCD are briefly discussed.