Catalysis of Dynamical Symmetry Breaking by a Magnetic Field

TL;DR

A magnetic field strongly induces dynamical chiral symmetry breaking in fermionic systems across different dimensions, leading to mass generation even with weak interactions, due to effective dimensional reduction.

Contribution

This paper demonstrates how magnetic fields catalyze symmetry breaking and mass generation in fermionic models, extending understanding of magnetic effects in quantum field theories.

Findings

Magnetic fields induce fermion mass generation at weak coupling.

Dimensional reduction explains the catalysis effect.

Applications discussed include inhomogeneous magnetic field configurations.

Abstract

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 mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction $D/rightarrow D-2$ in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio model and QED. Possible applications of this effect and its extension to inhomogeneous field configurations are discussed.