Gauge independence and chiral symmetry breaking in a strong magnetic field

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger–Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of the truncated Schwinger–Dyson equations evaluated on the fermion mass shell, is manifestly gauge independent.