Dynamical chiral symmetry breaking by a magnetic field in QED

It is shown that chiral symmetry is spontaneously broken by a constant magnetic field in QED. The dynamical mass of fermions (energy gap in the fermion spectrum) is ${\mathit{m}}_{\mathrm{dyn}}$≃C √eB exp[-(π/α${)}^{1/2}$], where B is the magnetic field, the constant C is of order one, and α=${\mathit{e}}^2$/4π is the renormalized coupling constant. Possible applications of this effect are discussed.