We show that effective field theory techniques can be applied
in the high temperature T plasmas to
improve the accuracy of the physics of the hard scales ( or scales of order T).
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
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 equilibrium, when for most on-shell particles p ~ 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. We also show how with
the OSEFT one can derive quantum corrections
to classical transport equations.