Abstract
The catalysis of chiral symmetry breaking by an applied constant magnetic field 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 chiral symmetry, generating a dynamical mass even at the weakest attractive interaction between fermions. For antiperiodic boundary conditions the effect of the finite third dimension is to counteract the chiral symmetry breaking.
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