Large N dynamics in QED in a magnetic field -: art. no. 107703

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 = root\eB\. For N of the order of N-thr or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with a cutoff of the order of root\eB\ and the dimensional coupling constant Gsimilar to1/(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 (α) over tilde (b)=Nalpha(b)<<1) from a strong coupling one (with (α) over tilde (b)greater than or similar to1) and is of the order of 1/alpha(b).