New Angular Momentum Conservation Laws for Gauge Fields in QED

TL;DR

This paper derives new local conservation laws for angular momentum in quantum electrodynamics, revealing detailed spin and orbital angular momentum dynamics and their exchange in light-matter interactions.

Contribution

It introduces a novel local conservation law for angular momentum in QED and formulates coupled motion equations for spin and orbital angular momentum densities.

Findings

Derived a local conservation law for angular momentum in QED.

Formulated coupled equations for spin and orbital angular momentum.

Applied results to classical electrodynamics scenarios like plane wave interference.

Abstract

Quantum electrodynamics (QED) deals with the relativistic interaction of bosonic gauge fields and fermionic charged particles. In QED, global conservation laws of angular momentum for light-matter interactions are well-known. However, local conservation laws, i.e. the conservation law of angular momentum at every point in space, remain unexplored. Here, we use the QED Lagrangian and Noether's theorem to derive a new local conservation law of angular momentum for Dirac-Maxwell fields in the form of the continuity relation for linear momentum. We separate this local conservation law into four coupled motion equations for spin and orbital angular momentum (OAM) densities. We introduce a helicity current tensor, OAM current tensor, and spin-orbit torque in the motion equations to shed light on on the local dynamics of spin-OAM interaction and angular momentum exchange between Maxwell-Dirac fields. We elucidate how our results translate to classical electrodynamics using the example of plane wave interference as well as a dual-mode optical fiber. Our results shine light on phenomena related to the spin of gauge bosons.