Dimensional Reduction and Dynamical Chiral Symmetry Breaking by a Magnetic Field in $3+1$ Dimensions

Abstract

It is shown that in $3+1$ dimensions, a constant magnetic field is a catalyst of dynamical chiral symmetry breaking, leading to generating a fermion mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction $D\to D-2$ ($3+1\to 1+1$) in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio model. Possible applications of this effect are briefly discussed.

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