The topology, geometry, and angular momentum of cold plasma waves

It was recently discovered that plasma waves possess topologically protected edge modes, indicating the existence of topologically nontrivial structures in the governing equations. Here we give a rigorous study of the underlying topological vector bundle structure of cold unmagnetized plasma waves and show that this topology can be used to uncover a number of new results about these waves. The topological properties of the electromagnetic waves mirror those recently found for photons and other massless particles. We show that there exists an explicit globally smooth polarization basis for electromagnetic plasma waves -- surprisingly, this does not violate the hairy ball theorem. The rotational symmetry of the waves gives a natural decomposition into topologically nontrivial $R$ and $L$ circularly polarized electromagnetic waves and the topologically trivial electrostatic Langmuir waves. The existence of topologically nontrivial waves, despite the effective mass introduced by the plasma, is related to the resonance of electrostatic and electromagnetic waves. We show that the eigenstates of the angular momentum operator are the spin-weighted spherical harmonics, giving a novel globally smooth basis for plasma waves. The sparseness of the resultant angular momentum multiplet structure illustrates that the angular momentum does not split into well-defined spin and orbital parts. However, we demonstrate that the angular momentum admits a natural decomposition, induced by the rotational symmetry, into two quasi-angular momentum components, termed helicity and orbital quasi-angular momentum. Although these operators do not generate physical rotations and therefore do not qualify as true angular momentum operators, they are gauge invariant, well-defined, and appear to be experimentally relevant.