Covariant calculations at finite temperature: The relativistic plasma

It is shown that finite-temperature calculations in field theory are manifestly Lorentz covariant at all stages if the Minkowski-space form of the temperature-dependent propagators is used and if the four-velocity u_ of the heat bath is taken into account. New tensor structures involving u_ generally arise but are severely constrained by covariant current conservation. A complete high-temperature (T) expansion of the vacuum polarization tensor for non-Abelian gauge theories is computed to order g^2 and displays the separate dependence on frequency and wave number k that occurs at finite temperature. A covariant phenomenology of "electric" and "magnetic" properties is applied to the collective plasma effects, characterized by a plasma frequency {₏}^2= (N₅+2N) {g^2T^2}6 for SU (N) with N₅ fermions. The longitudinal normal modes of the "electric" field exist only for >₏; for ₏; for <₏ both transverse "electric" and "magnetic" fields are shielded except for the static (=0) case.