Abstract
We study the neutrino anti-neutrino pair synchrotron emission from electrons and protons in a relativistic quantum approach. This process occurs only under a strong magnetic field, and it is considered to be one of effective processes for neutron star cooling. In this work we calculate the luminosity of the neutrino anti-neutrino pairs emitted from neutron-star-matter with a magnetic field of about 10^{15} G. We find that the energy loss is much larger than that of the modified Urca process. The neutrino anti-neutrino pair emission processes in strong magnetic fields is expected to contribute significantly to the cooling of the magnetars.
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