Expectation value of the axial-vector current in the external electromagnetic field

We are calculated the expectation value of the axial-vector current induced by the vacuum polarization effect of the Dirac field in constant external electromagnetic field. In calculations we use Schwinger's proper time method. The effective Lagrangian has very simple Lorenz invariant form. Along with the anomaly term, it also contains two Lorenz invariant terms. The result is compared with our previous calculation of the photon - Z boson mixing in the magnetic field.