Fermionic Collective Modes of an Anisotropic Quark-Gluon Plasma

We determine the fermionic collective modes of a quark-gluon plasma which is anisotropic in momentum space. We calculate the fermion self-energy in both the imaginary- and real-time formalisms and find that numerically and analytically (for two special cases) there are no unstable fermionic modes. In addition we demonstrate that in the hard-loop limit the Kubo-Martin-Schwinger condition, which relates the off-diagonal components of the real-time fermion self-energy, holds even for the anisotropic, and therefore non-equilibrium, quark-gluon plasma considered here. The results obtained here set the stage for the calculation of the non-equilibrium photon production rate from an anisotropic quark-gluon plasma.