Dispersion in a relativistic degenerate electron gas

Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically and non-relativistically. The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and non-relativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the non-relativistic treatment has a non-physical feature near the cutoff frequency for large Fermi momenta, and this is attributed to an incorrect treatment of the electron spin. We find (with two important provisos) that one-photon pair creation is allowed in superdense plasmas, implying relatively strong coupling between transverse waves and pair creation.