Radiative and non-perturbative corrections to the electron mass and the anomalous magnetic moment in the presence of an external magnetic field of arbitrary strength

Using the Ritus eingenfunction method we compute corrections to the electron mass m_{0} in the presence of a moderate magnetic field eB ~ m_0^2. From this we obtain an expression for the anomalous magnetic moment near the critic field. For this we solved numerically the Schwinger-Dyson equations in the rainbow approximation including all Landau levels without make any assumption respect to the field strength.