The theory of the magnetic catalysis of chiral symmetry breaking in QED is
developed. An approximation for the Schwinger-Dyson equations describing re
liably this phenomenon is established, i.e. it is shown that there exists a
consistent truncation of those equations in this problem. The equations ar
e solved both analytically and numerically, and the dynamical mass of fermi
ons is determined. (C) 1999 Elsevier Science B.V. All rights reserved.