Screening and antiscreening in anisotropic QED and QCD plasmas

We use a transport-theory approach to construct the static propagator of a gauge boson in a plasma with a general axially- and reflection-symmetric momentum distribution. Non-zero magnetic screening is found if the distribution is anisotropic, confirming the results of a closed-time-path-integral approach. We find that the electric and magnetic screening effects depend on both the orientation of the momentum carried by the boson and the orientation of its polarization. In some orientations there can be antiscreening, reflecting the instabilities of such a medium. We present some fairly general conditions on the dependence of these effects on the anisotropy.