  Relativistic effects on dispersion in a degenerate electron gas are discussed
by comparing known response functions derived relativistically (by Jancovici)
and nonrelativistically (by Lindhard). 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 nonrelativistic case, with the
main relativistic effects being on the Fermi speed and the cutoff frequency.
For transverse waves the nonrelativistic treatment has a nonphysical 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.
