Dynamical Chiral Symmetry Breaking by a Magnetic Field in QED

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