Chiral Symmetry Restoration and Parity Mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study how the modification of the quark condensate affects the coupling constants of the axial cur- rent, namely the pion decay constant and the nucleonic axial one. In the second case and in a dense medium, we express the renormalization as a meson exchange current. By doing so we show what part of the scalar den- sity of the quarks contributes to the renormalization. We give an esti- mate for the quenching of the axial coupling constant linked to chiral symmetry restoration.