  We show that effective field theory techniques can be applied in the high
temperature $T$ regime of plasmas to improve the accuracy of the physics of the
hard scales (or scales of order $T$), and as a by-product, also that of the
soft scales (or scales of order $gT$). At leading order in the coupling
constant the hard scales of the plasma can be viewed as on-shell classical
particles. Based on this observation, and without any reference to the state of
the system, we derive an effective field theory describing the quantum
fluctuations around an on-shell fermion with energy $p$, described as a set of
high dimension operators over the on-shell energy $p$. When applied to systems
close to thermal equilibrium, where for most on-shell particles $p \sim T$, we
show that the on-shell effective field theory (OSEFT) properly describes the
HTL photon polarization tensor of QED, and its 1/T corrections. For the soft
scales the first non-vanishing power correction turns out to be a perturbative
correction to the HTL result.

High Energy Physics - Phenomenology