Neutrino Bremsstrahlung in an Intense Magnetic Field

In this paper we present the neutrino luminosity due to a completely relativistic electron gas in the presence of an intense magnetic field. The neutrino emission rate is determined rigorously, under the assumption of the $V-A$ theory of universal weak Fermi interaction, by standard field-theoretical methods. It is shown that the neutrino radiation rate can be expressed as a function of temperature, density, and the field-strength parameter $\Theta =\frac{H}{H_c}$, where $H_c=\frac{m^2{c}^3}{e\hslash }=4.414\mathrm{}\times {10}^{13}$ G. Comparisons are made with previous approximate results due to others, and the reasons for discrepancies are discussed.