Large N dynamics in QED in a magnetic field

Abstract

The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of 1/N expansion. The existence of a threshold value N_{thr}, dividing the theories with essentially different dynamics, is established. For the number of flavors N << N_{thr}, the dynamical mass is very sensitive to the value of the coupling constant α_b, related to the magnetic scale μ= |eB|. For N of order N_{thr} or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with cutoff of order |eB| and the dimensional coupling constant G \sim 1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially α_b independent (the dynamics with an infrared stable fixed point). The value of N_{thr} separates a weak coupling dynamics (with \tildeα_b \equiv Nα_b << 1) from a strong coupling one (with \tildeα_b \gtrsim 1) and is of order 1/α_b.

4 pages, REVTeX