Equilibrium and Non-Equilibrium Hard Thermal Loop Resummation in the Real Time Formalism

We investigate the use of the hard thermal loop (HTL) resummation technique in non-equilibrium field theory. We use the Keldysh representation of the real time formalism (RTF). We derive the HTL photon self energy and the resummed photon propagator. We show that no pinch singularities appear in the non-equilibrium HTL effective propagator. We discuss a possible regularization mechanism for these singularities at higher orders. As an example of the application of the HTL resummation method within the RTF we discuss the damping rate of a hard electron.

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