Article,
Covariant calculations at finite temperature: The relativistic plasma
Physical Review D, 26 (6): 1394--1407 (September 1982)
DOI: 10.1103/physrevd.26.1394
Abstract
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 uμ of the heat bath is taken into account. New tensor structures involving uμ generally arise but are severely constrained by covariant current conservation. A complete high-temperature (T≫m) expansion of the vacuum polarization tensor for non-Abelian gauge theories is computed to order g2 and displays the separate dependence on frequency ω 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 ωp2=(Nf+2N)g2T2/6 for SU(N) with Nf fermions. The longitudinal normal modes of the "electric" field exist only for ω>ωp; for ω<ωp all "electric" fields are screened. The transverse normal modes are plane waves along Ẽ×B̃ for ω>ωp; for ω<ωp both transverse "electric" and "magnetic" fields are shielded except for the static (ω=0) case.
