Effective kinetic theory for high temperature gauge theories

Quasiparticle dynamics in relativistic plasmas associated with hot,weakly-coupled gauge theories (such as QCD at asymptotically high temperature$T$) can be described by an effective kinetic theory, valid on sufficientlylarge time and distance scales. The appropriate Boltzmann equations depend oneffective scattering rates for various types of collisions that can occur inthe plasma. The resulting effective kinetic theory may be used to evaluateobservables which are dominantly sensitive to the dynamics of typicalultrarelativistic excitations. This includes transport coefficients(viscosities and diffusion constants) and energy loss rates. We show how toformulate effective Boltzmann equations which will be adequate to compute suchobservables to leading order in the running coupling $g(T)$ of high-temperaturegauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposedin the literature, a leading-order treatment requires including both $2<->2$particle scattering processes as well as effective ``$1<->2$'' collinearsplitting processes in the Boltzmann equations. The latter account for nearlycollinear bremsstrahlung and pair production/annihilation processes which takeplace in the presence of fluctuations in the background gauge field. Oureffective kinetic theory is applicable not only to near-equilibrium systems(relevant for the calculation of transport coefficients), but also to highlynon-equilibrium situations, provided some simple conditions on distributionfunctions are satisfied.Comment: 40 pages, new subsection on soft gauge field instabilities adde