Coherent neutrino radiation in supernovae at two loops

We develop a neutrino transport theory, in terms of the real-time non-equilibrium Green's functions, which is applicable to physical conditions arbitrary far from thermal equilibrium. We compute the coherent neutrino radiation in cores of supernovae by evaluating the two-particle-two-hole (2p-2h) polarization function with dressed propagators. The propagator dressing is carried out in the particle-particle channel to all orders in the interaction. We show that at two loops there are two distinct sources of coherence effects in the bremsstrahlung. One is the generically off-shell intermediate state propagation, which leads to the Landau-Pomeranchuk-Migdal type suppression of radiation. We extend previous perturbative results, obtained in the leading order in quasiparticle width, by deriving the exact non-perturbative expression. A new contribution due to off-shell finial/initial baryon states is treated in the leading order in the quasiparticle width. The latter contribution corresponds to processes of higher order than second order in the virial expansion in the number of quasiparticles. At 2p-2h level, the time component of the polarization tensor for the vector transitions vanishes identically in the soft neutrino limit. Vector current thereby is conserved. The contraction of the neutral axial vector current with tensor interaction among the baryons leads to a non-vanishing contribution to the bremsstrahlung rate. These rates are evaluated numerically for finite temperature pure neutron matter at and above the nuclear saturation density.