Electromagnetic properties of neutrinos in a background of electrons

Using covariant methods we calculate the neutrino electromagnetic vertex in a gas of electrons to lowest order in a loop expansion and to the lowest order in $\frac{1}{M_W^2}$. The new induced terms, while they are chirality preserving, yield additional contributions to the dipole moments in the nonrelativistic limit. These are identical for particles and antiparticles and so need not vanish for Majorana neutrinos. As applications of our formulas, the expression for the $\mathrm{plasmon}\to \nu \overline{\nu }$ decay rate is rederived and the dispersion relation of a massless neutrino propagating in matter in the presence of an external magnetic field is determined. The possible implications of these effects are considered.