Abstract
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 $V\ensuremath{-}A$ 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 $\ensuremath{\Theta}=\frac{H}{{H}_{c}}$, where ${H}_{c}=\frac{{m}^{2}{c}^{3}}{e\ensuremath{\hbar}}=4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}$ G. Comparisons are made with previous approximate results due to others, and the reasons for discrepancies are discussed.
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