Neutrino-electron processes in a strongly magnetized thermal plasma

We present a new method of calculating the rate of neutrino-electron interactions in a strong magnetic field based on finite temperature field theory. Using this method, in which the effect of the magnetic field on the electron states is taken into account exactly, we calculate the rates of all of the lowest order neutrino-electron interactions in a plasma. As an example of the use of this technique, we explicitly calculate the rate at which neutrinos and antineutrinos annihilate in a highly magnetized plasma, and compare that to the rate in an unmagnetized plasma. The most important channel for energy deposition is the gyromagnetic absorption of a neutrino-antineutrino pair on an electron or positron in the plasma ($\nu\bar{\nu} e^\pm\leftrightarrow e^\pm$). Our results show that the rate of annihilation increases with the magnetic field strength once it reaches a certain critical value, which is dependent on the incident neutrino energies and the ambient temperature of the plasma. It is also shown that the annihilation rates are strongly dependent on the angle between the incident particles and the direction of the magnetic field. If sufficiently strong fields exist in the regions surrounding the core of a type II supernovae or in the central engines of gamma ray bursts, these processes will lead to more efficient plasma heating mechanism than in an unmagnetized medium, and moreover, one which is intrinsically anisotropic.