A mean field theory for the cold quark gluon plasma

A hot and strongly interacting quark gluon plasma (QGP) has been observed in heavy ion collisions at RHIC. Quarks and gluons in a deconfined phase might also exist in the core of compact stars. We shall assume here that the cold QGP is also a strongly interacting system. The strong interactions may be partly due to non-perturbative effects, which survive after the deconfinement transition and which can be related with the non-vanishing gluon condensates in the QGP. In this work, starting from the QCD Lagrangian we perform a gluon field decomposition in low ('soft') and high ('hard') momentum components, we make a mean field approximation with spatial and time dependence for the hard gluons and take the matrix elements of the soft gluon fields in the plasma. The latter are related to the gluon condensates. We derive an analytical expression for the equation of state, which is compared with the MIT bag model one. The effect of the condensates is to soften the equation of state whereas the hard gluons significantly increase the energy density and the pressure.