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 \alpha_b, related to the magnetic scale \mu = |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 \alpha_b independent (the dynamics with an infrared stable fixed point). The value of N_{thr} separates a weak coupling dynamics (with \tilde{\alpha}_b \equiv N\alpha_b << 1) from a strong coupling one (with \tilde{\alpha}_b \gtrsim 1) and is of order 1/\alpha_b.
Keywords
Cite
@article{arxiv.hep-ph/0304059,
title = {Large N dynamics in QED in a magnetic field},
author = {V. P. Gusynin and V. A. Miransky and I. A. Shovkovy},
journal= {arXiv preprint arXiv:hep-ph/0304059},
year = {2009}
}
Comments
4 pages, REVTeX