The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops

Abstract

We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling $g$ is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale $gT$, which is well separated from the typical energy of single particle excitations which is the temperature $T$. We show that the plasma particles provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in $g$, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. As a by-product, the ``hard thermal loops'' emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. The effect of collisions among the hard particles is also studied, in particular in relation with the effective theory for ultrasoft excitations, with momenta $\sim g^2T$.