On chiral symmetry breaking by external magnetic fields in QED${}_3$

Abstract

A recent result of Gusynin, Miransky and Shovkovy concerning chiral symmetry breaking by a constant external magnetic field in parity-invariant three-dimensional QED is generalised to the case of inhomogeneous fields by relating the phenomenon to the zero modes of the Dirac equation. Virtual photon radiative corrections and four-dimensional QED are briefly discussed.

Comments: 10 page Revtex file. Minor corrections, mainly in the discussion leading upto Eqs.(10,11) and the references. Version to be published