  We study the electromagnetic properties of a system that consists of an
electron background and a neutrino gas that may be moving or at rest, as a
whole, relative to the background. The photon self-energy for this system is
characterized by the usual transverse and longitudinal polarization functions,
and two additional ones which are the focus of our calculations, that give rise
to birefringence and anisotropic effects in the photon dispersion relations.
Expressions for them are obtained, which depend on the neutrino number
densities and involve momentum integrals over the electron distribution
functions, and are valid for any value of the photon momentum and general
conditions of the electron gas. Those expressions are evaluated explicitly for
several special cases and approximations which are generally useful in
astrophysical and cosmological settings. Besides studying the photon dispersion
relations, we consider the macroscopic electrodynamic equations for this
system, which involve the standard dielectric and permeability constants plus
two additional ones related to the photon self-energy functions. As an
illustration, the equations are used to discuss the evolution of a magnetic
field perturbation in such a medium. This particular phenomena has also been
considered in a recent work by Semikoz and Sokoloff as a mechanism for the
generation of large-scale magnetic fields in the Early Universe as a
consequence of the neutrino-plasma interactions, and allows us to establish
contact with a specific application in a well defined context, with a broader
scope and from a very different point of view.
