Gauge Structure and Semi-Classical Aspects of Hard Thermal Loops

Hard thermal loops play a central role in the theory of long wavelength excitations of a quark-gluon plasma. We show in this paper how our recent derivation of their generating functional from the Dyson-Schwinger equations sheds light on their semi-classical nature and their remarkable gauge structure. In particular, we show that our kinetic equations can be written in terms of auxiliary gauge fields with zero curvature. Remarkably, the latter property determines entirely the dynamics in the kinematical regime of hard thermal loops. This explains in particular why the generating functional could have been obtained by Taylor and Wong from gauge invariance considerations. It also clarifies the role of Chern-Simons theory in this context.