DIMENSIONAL REDUCTION AND CATALYSIS OF DYNAMICAL SYMMETRY-BREAKING BYA MAGNETIC-FIELD

It is shown that a constant magnetic field in 3+1 and 2+1 dimensions i s a strong catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion dynamical mass even at the weakest attract ive interaction between fermions. The essence of this effect is the di mensional 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. In the NJL model in a magnetic field, the low-ene rgy effective action and the spectrum of long-wavelength collective ex citations are derived. In QED (in ladder and improved ladder approxima tions) the dynamical mass of fermions (energy gap in the fermion spect rum) is determined. Possible applications of this effect and its exten sion to inhomogeneous field configurations are discussed.