V. P. Gusynin, V. A. Miransky, I. A. Shovkovy
Published 1995-09-18, updated 1996-01-18Version 2
It is shown that 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 $D\to D-2$ 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--energy effective action and the spectrum of long wavelength collective excitations are derived. In QED (in ladder and improved ladder approximations) the dynamical mass of fermions (energy gap in the fermion spectrum) is determined. Possible applications of this effect and its extension to inhomogeneous field configurations are discussed.
Comments: 54 pages, uuencoded LaTeX. Two figures included. The final, extended, version. Accepted for publication in Nuclear Physics B
Journal: Nucl.Phys. B462 (1996) 249-290
Dimensional reduction and the generalized pion in a magnetic field within the NJL model
$N=1$ trinification from dimensional reduction of $N=1$, $10D$ $E_8$ over $SU(3)/U(1)\times U(1)\times Z_3$ and its phenomenological consequences
Higher-order corrections to phase-transition parameters in dimensional reduction
