More on difference between angular momentum and pseudo-angular momentum

TL;DR

This paper clarifies the distinction between angular momentum and pseudo-angular momentum in field theory, correcting previous expressions for linear systems and analyzing electromagnetic angular momentum as pseudo-angular momentum.

Contribution

It derives the correct rotation symmetry and angular momentum for linear elastic systems and reinterprets electromagnetic angular momentum as pseudo-angular momentum.

Findings

Corrected angular momentum expression for linear elastic systems.

Identified electromagnetic angular momentum as pseudo-angular momentum.

Derived conserved electromagnetic momentum and angular momentum in vacuum.

Abstract

We extend the discussion on the difference between angular momentum and pseudo-angular momentum in field theory. We show that the often quoted expressions in [Phys.Rev.B 103, L100409 (2021)] only apply to a non-linear system, and derive the correct rotation symmetry and the corresponding angular momentum for a linear elastic system governed by Navier-Cauchy equation. By mapping the concepts and methods for the elastic wave into electromagnetic theory, we argue that the renowned canonical and Benlinfante angular momentum of light are actually pseudo-angular momentum. Then, we derive the ``Newtonian" momentum $\int \text{d}^3 x\boldsymbol{E}$ and angular momentum $\int \text{d}^3 x (\boldsymbol{r}\times\boldsymbol{E})$ for a free electromagnetic wave, which are conserved quantities during propagation in vacuum.