Ohm's Law for a Relativistic Pair Plasma
  We derive the fully relativistic Ohm's law for an electron-positron plasma. The absence of non-resistive terms in Ohm's law and the natural substitution of the 4-velocity for the velocity flux in the relativistic bulk plasma equations do not require the field gradient length scale to be much larger than the lepton inertial lengths, or the existence of a frame in which the distribution functions are isotropic. 
Eric G. Blackman and George B. Field (Harvard Univ.)