Non-Equilibrium HTL Resummation

We present an extension of the HTL resummation technique to non-equilibrium situations, starting from the real time formalism in the Keldysh representation. As an example we calculate the HTL photon self energy, from which we derive the resummed photon propagator. This propagator is applied to the computation of the interaction rate of a hard electron in a non-equilibrium QED plasma. In particular we show the absence of of pinch singularities in these quantities. Finally we show that the Ward identities relating the HTL electron self energy to the HTL electron-photon vertex hold as in equilibrium.