Plasmons from a gauge invariant effective action for hot gluons

The one-loop effective action for a gluon plasma is calculated in a general covariant background field gauge. The result is expressed in terms of the dielectric constant and the magnetic permeability, which immediately yields dispersion relations for both longitudinal and transverse plasma waves. The plasma frequency is gauge fixing independent and agrees with earlier calculations, while the plasma damping constant is gauge fixing dependent and negative definite. We argue that the result in Landau gauge is of physical significance, and that the calculated exponential growth of the plasmon amplitude is a signal for the breakdown of perturbation theory at scales of order ∼ g²T. The relevance of this for the dynamical description of the quark-gluon plasma is discussed.