The catalysis of chiral symmetry breaking by an applied constant magnetic f
ield and in the presence of boundaries along third axis is investigated in
the four-dimensional Nambu-Jona-Lasinio model. It is shown that in case of
periodic boundary conditions for fermions the magnetic field breaks the chi
ral symmetry, generating a dynamical mass even at the weakest attractive in
teraction between fermions. For antiperiodic boundary conditions the effect
of the finite third dimension is to counteract the chiral symmetry breakin
g. (C) 1999 Published by Elsevier Science B.V. All rights reserved.