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 Nthr, dividing the theories with essentially different dynamics, is established. For the number of flavors N << Nthr, the dynamical mass is very sensitive to the value of the coupling constant αb, related to the magnetic scale μ = |eB|. For N of order Nthr or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with cutoff of order |eB| and the dimensional coupling constant G 1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially αb independent (the dynamics with an infrared stable fixed point). The value of Nthr separates a weak coupling dynamics (with αb Nαb << 1) from a strong coupling one (with αb 1) and is of order 1/αb.
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