Residual gauge theory for quanta of surface plasmons

We develop a gauge-theoretical framework to investigate the quanta of surface plasmons. Our formulation, based on quantum electrodynamics, highlights the importance of residual gauge symmetry. We emphasize that residual gauge symmetry, which imposes constraint equations on physical states, is fundamentally linked to Joule heating. This framework is applied to metals, semiconductors, and quantum Hall states, suggesting the presence of a latent transverse electric mode and that the quanta have the ability to maintain light-matter entanglement.