Instantaneous chiral quark model for relativistic mesons in a hot and dense medium

A chiral quark model with covariant instantaneous interactions is formulated using relativistic thermodynamic Green functions. The approach is applied to the description of mesons as relativistic bound states in hot and dense quark matter. The Schwinger-Dyson equation for the quark-mass operator and the Salpeter equations for quark-antiquark bound states are obtained for a nonlocal covariant four-point interaction kernel. Special attention is paid to the medium modification of meson properties as a function of their total momentum. Numerical results for the pion mass and the pion decay constant at finite temperature are presented for the special case of a separable interaction. We obtain a ''protection'' of the pseudoscalar bound state against medium influence due to the finite (thermal) velocity relative to the surrounding matter. ((orig.))