Fermion Thermal Field Theory for a Rotating Plasma (with Applications to Neutron Stars)

Abstract: This paper provides a systematic and complete study of thermal field theory with fermion fields of any kind for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also average angular momentum. This extends a previous study that focused on scalar fields, to all fermion-scalar theories. Both Dirac and Majorana fermions and both Dirac and Majorana masses are covered. A general technique to compute ensemble averages is provided. Path-integral methods are developed to study thermal Green's functions (with an arbitrary number of points) in generic interacting fermion-scalar theories, which cover both the real-time and imaginary-time formalism. These general results are applied to physical situations typical of neutron stars, which are often quickly rotating: the Fermi surface and Fermi momentum, the average energy, number density and angular momentum for degenerate fermions and particle production (such as neutrino production from rotating neutron stars, e.g. pulsars). In particular, it is shown that the neutrino production rate due to the direct URCA (DU) processes grows indefinitely as the angular velocity approaches the inverse linear size of the plasma and, therefore, rotation can significantly increase this rate.