Currents and local gauge symmetries

The current-algebra properties of gauge field theories are investigated. First, we consider a unified gauge field model of strong, weak, and electromagnetic interactions, which is a natural extension of the σ model combined with the Weinberg-Salam model. The violation of CP invariance is forbidden, and isospin is only broken by electromagnetic interactions. The pion is possibly a pseudo-Goldstone boson, which picks up its mass from weak and electromagnetic interactions. In the physical gauge the weak axial-vector currents are not of the canonical form, thus invalidating the current-algebra hypothesis. However, further analysis based on generalized Ward-Takahashi identities shows that the divergence equations are not affected. Furthermore, we discuss in which case the partially conserved axial-vector current approximation can be justified.