Abstract
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 ${\mathit{m}}_{\mathrm{dyn}}$\ensuremath{\simeq}C \ensuremath{\surd}eB exp[-(\ensuremath{\pi}/\ensuremath{\alpha}${)}^{1/2}$], where B is the magnetic field, the constant C is of order one, and \ensuremath{\alpha}=${\mathit{e}}^{2}$/4\ensuremath{\pi} is the renormalized coupling constant. Possible applications of this effect are discussed.
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