Gauge field theory methods for ultra-degenerate and ultra-relativistic plasmas

We present a gauge field theory approach for the description of ultra-degenerate and ultra-relativistic plasmas. Based on the analogy with the finite-temperature case, we first calculate the hard loops at finite density necessary for the resummation of long-range effects. We then analyze the scattering rates in the plasma and find that the collective phenomena are mainly supported by the photons. We apply these considerations to the energy loss rates of axion-like particles coupled to the electromagnetic fields in supernovae, red giants and white dwarves and we obtain new bounds on the effective couplings.