Electromagnetic properties of a neutrino stream - art. no. 113008

In a medium that contains a neutrino background in addition to matter parti cles, the neutrinos contribute to the photon self-energy as a result of the effective electromagnetic vertex that they acquire in the presence of matt er. We calculate the contribution to the photon self-energy in a dense plas ma, due to the presence of a gas of charged particles, or neutrinos, which moves as a whole relative to the plasma. General formulas for the transvers e and longitudinal components of the photon polarization tensor are obtaine d in terms of the momentum distribution functions of the particles in the m edium, and explicit results are given for various limiting cases of practic al interest. The formulas are used to study the electromagnetic properties of a plasma that contains a beam of neutrinos. The transverse and longitudi nal photon dispersion relations are studied in some detail. Our results do not support the idea that neutrino streaming instabilities can develop in s uch a system. We also indicate how the phenomenon of optical activity of th e neutrino gas is modified due to the velocity of the neutrino background r elative to the plasma. The general approach and results can be adapted to s imilar problems involving relativistic plasmas and high-temperature gauge t heories in other environments.