Neutrino-electron processes in a strongly magnetized thermal plasma

We present a new method of calculating the rate of neutrino-electroninteractions in a strong magnetic field based on finite temperature fieldtheory. Using this method, in which the effect of the magnetic field on theelectron states is taken into account exactly, we calculate the rates of all ofthe lowest order neutrino-electron interactions in a plasma. As an example ofthe use of this technique, we explicitly calculate the rate at which neutrinosand antineutrinos annihilate in a highly magnetized plasma, and compare that tothe rate in an unmagnetized plasma. The most important channel for energydeposition is the gyromagnetic absorption of a neutrino-antineutrino pair on anelectron or positron in the plasma ($\nu\bar{\nu} e^\pm\leftrightarrow e^\pm$).Our results show that the rate of annihilation increases with the magneticfield strength once it reaches a certain critical value, which is dependent onthe incident neutrino energies and the ambient temperature of the plasma. It isalso shown that the annihilation rates are strongly dependent on the anglebetween the incident particles and the direction of the magnetic field. Ifsufficiently strong fields exist in the regions surrounding the core of a typeII supernovae or in the central engines of gamma ray bursts, these processeswill lead to more efficient plasma heating mechanism than in an unmagnetizedmedium, and moreover, one which is intrinsically anisotropic.Comment: 17 pages, 8 figures, minor corrections, references added, to be published in Phys. Rev.