QED effective action in a constant electromagnetic field under conditions of possible Lorentz invariance violation in the Dirac equation

This paper is devoted to the calculation of corrections to QED effective action associated with the axial-vector condensate $b^\mu$, which violate the Lorentz invariance. It was shown that the linear in $b^\mu$ contribution to the 1-loop effective action (Chern-Simons term) is absent in the case of a constant electromagnetic field. The contribution, which is quadratic in $b^\mu$, was calculated for the cases of both constant magnetic and electric fields. Asymptotic estimates of the quadratic in $b^\mu$ term for strong and weak field strengths were obtained.