Axial and Vector Correlator Mixing in Hot and Dense Hadronic Matter

We study the manifestations of chiral symmetry restoration which have a significance for the parity mixing. Restricting to pions and nucleons we establish a formalism for the expression of the vector correlator, which displays the mixing of the axial correlator into the vector one and unifies the cases of the heat bath and the dense medium. We give examples of mixing cross-sections. We also establish a link between the energy integrated mixing cross-sections and the pion scalar density which governs the quenching factors of coupling constants, such as the pion decay one, as well as the quark condensate evolution.