QED in a strong external magnetic field: Beyond the constant mass approximation - art. no. 105017

We solve the Schwinger-Dyson equations for QED in 2+1 or 3+1 dimensions in the presence of a strong homogeneous external magnetic field. The magnetic field is assumed strong enough, so that the lowest Landau level approximati on holds, but the usual assumption of a momentum-independent self-energy is not made. In 2+1 dimensions, the scaling with logarithm changes to a squar e root dependence on the magnetic field, but the most spectacular result ta kes place in 3+1 dimensions, where the constant mass approximation turns ou t to be unreliable and the (momentum-dependent) dynamical mass is larger by several orders of magnitude compared to what has been found until now usin g the constant mass approximation.