Weak currents in Fermi systems

In the framework of a relativistic field theory for the many-body system we use the hypothesis of a partially-conserved axial-vector current to relate weak-interaction coupling constants to strong-interaction parameters. The density-dependent renormalizations of weak-interaction coupling constants are investigated using the Ward-Takahashi identities of the σ-model. We compare the renormalization procedures for the vector current and for the axial-vector current and generally discuss differences between renormalizations at zero density and in the medium.