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 Schwingers proper time method. The effective Lagrangia
n 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.
