Electron self-energy in strong magnetic field: summation of double logarithmic terms

We study the electron self-energy in a strong magnetic field when the parameter η≡(α/2π)ln2(eB/m20)∼1 and explore the transition between the perturbative regime η≪1 and the nonperturbative massless QED regime η≫1 where chiral symmetry is broken spontaneously and electrons acquire the dynamically induced mass.