A constant magnetic field in 3+1 and 2+1 dimensions is a strong catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion dynamical mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction D →D-2 in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio (NJL) model and QED. Possible applications of this effect and its extension to inhomogeneous field configurations are discussed.
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A 1996 study studied this question.