  The propagation of excitation modes in a relativistic ultradegenerate plasma
is modified by their interactions with the medium. These modifications can be
computed by evaluating their on-shell self-energy, which gives
(gauge-independent) dispersion relations. For modes with momentum close to the
Fermi momentum, the one-loop fermion self-energy is dominated by a diagram with
a soft photon in the loop. We find the one-loop dispersion relations for
quasiparticles and antiquasiparticles, which behave differently as a
consequence of their very different phase-space restrictions when they scatter
with the electrons of the Fermi sea. In a relativistic system, the unscreened
magnetic interactions spoil the normal Fermi liquid behavior of the plasma. For
small values of the Fermi velocity, we recover the non-relativistic dispersion
relations of condensed matter systems.
