Dynamical Chiral Symmetry Breaking by a Magnetic Field in QED

Abstract

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 $\alpha =e^2/4\pi$ is the renormalized coupling constant. Possible applications of this effect are discussed.

Comments: 12 pages, LaTeX. The final journal version (with minor corrections)