GAUGE STRUCTURE AND SEMICLASSICAL ASPECTS OF HARD THERMAL LOOPS

Hard thermal loops play a central role in the theory of long-wavelength excitations of a quark-gluon plasma. The recent derivation of their generating functional from the Dyson-Schwinger equations sheds light on their semi-classical nature and their particular gauge structure. We show in this paper that the zero-curvature gauge structure relating the generating functional to a Chem-Simons theory may be viewed as a two-dimensional projection of a more general, four-dimensional, structure which emerges, almost trivially, from the kinetic equations generating the hard thermal loops.