Soft collective excitations in hot gauge theories

Abstract

The long-wavelength excitations of a quark-gluon plasma at high temperature can be described as collective oscillations of gauge and fermionic average fields. We show that, at leading order in the coupling strength, the Dyson-Schwinger equations for the N-point functions reduce to a set of coupled equations for these average fields and their induced sources which involve only two-point functions. The equations for the two-point functions describe the dynamics of the hard plasma particles in the presence of soft background fields. They may be given the form of simple kinetic equations. Both the wavelength and the amplitude of the collective modes are controlled by the coupling strength, and we show that it is important to take this properly into account in order to obtain consistent equations of motion which are covariant under gauge transformations. By solving the kinetic equations for the two-point functions with well defined (i.e. retarded or advanced) boundary conditions, we obtain the induced currents in closed forms. These act as generating functionals for the one-particle irreducible amplitudes with soft external lines, and yield in particular all the so called “hard thermal loops” identified in the diagrammatic analysis.