Semi-classical transport theory for non-Abelian plasmas

We review a semi-classical transport theory for non-Abelian plasmas based on a classical picture of coloured point particles. Within this formalism, kinetic equations for the mean particle distribution, the mean fields and their fluctuations are obtained using an ensemble-average in phase space. The framework permits the integrating-out of fluctuations in a systematic manner. This leads to the derivation of collision integrals, noise sources and fluctuation-induced currents for the effective transport equations of QCD. Consistency with the non-Abelian gauge symmetry is established, and systematic approximation schemes are worked out. In particular, the approach is applicable to both in- and out-of-equilibrium plasmas. The formalism is applied explicitly to a hot and weakly coupled QCD plasma slightly out of equilibrium. The physics related to Debye screening, Landau damping or colour conductivity is deduced in a very simple manner. Effective transport equations are computed to first and second order in moments of the fluctuations. To first order, they reproduce the seminal hard-thermal-loop effective theory. To second order, the fluctuations induce collisions amongst the quasi-particles, leading to a Langevin-type transport equation. A complementary Langevin approach is discussed as well. Finally, we show how the approach can be applied to dense quark matter systems. In the normal phase, the corresponding kinetic equations lead to the hard-dense-loop effective theory. At high density and low temperature diquark condensates are formed, changing the ground state of QCD. In the superconducting phase with two massless quark flavours, a transport equation for coloured excitations is given as well. Possible future applications are outlined.