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.Comment: 10 pages, 1 eps figure, version to appear in Annals of Physic
