Quantization of the free electromagnetic field implies quantization of its angular momentum

TL;DR

This paper demonstrates that applying gauge-invariant commutators to the electromagnetic field's momentum operators confirms their validity as quantum operators for angular momentum, supporting quantum mechanical calculations.

Contribution

It shows that the gauge-invariant Bohr-Rosenfeld commutators lead to proper quantum operators for electromagnetic angular momentum.

Findings

Operators satisfy canonical commutation relations

Validates use of these operators in quantum mechanics

Supports quantization of electromagnetic angular momentum

Abstract

It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.