Seminarium Teorii Oddziaływań Elementarnych

Introduction of the Faddeev-Popov ghosts to the Keldysh-Schwingerformalism describing equilibrium and non-equilibrium statistical systems ofquantum fields such as the quark-gluon plasma is considered. Theplasma is assumed to be homogeneous in a coordinate space but the momentumdistribution of plasma constituents is arbitrary. Withgenerating functional technique we derive the Slavnov-Taylor identities andone ofthem expresses the ghost Green's function, which we look for, through thegluon one. As an application, the Green's function of ghosts is used tocompute the gluon polarization tensor in the hard loop approximation whichappears to be automatically transverse, as required by the gauge invariance.