QCD perturbation theory at finite temperature/density and its application

In order to describe properties of an equilibrated quark-gluon plasma, QCD at finite temperature (and density) has to be considered. Besides lattice calculations, which can be applied only to static quantities at zero density, perturbative QCD has been used. At finite temperature, however, serious problems such as infrared divergent and gauge dependent results have been encountered. These difficulties can be (partially) avoided if one starts from effective Green functions constructed by resumming a certain class of diagrams (hard thermal loops). Within the last few years this improved perturbation theory (BraatenPisarski method) turned out to be a powerful tool for computing interesting quantities of the quark-gluon plasma phase. In the present talk a basic introduction to the Braaten-Pisarski method is provided and its applications and limits are reviewed. In particular, damping rates, the energy loss of energetic partons, thermalization times, the viscosity of the quark-gluon plasma, and the production of photons and dileptons are discussed.