The 1-loop self-energy of an electron in a strong external magnetic field revisited

Abstract

I calculate the 1-loop self-energy of the lowest Landau level of an electron of mass [Formula: see text] in a strong, constant and uniform external magnetic field [Formula: see text], beyond its always used truncation at [Formula: see text], [Formula: see text]. This is achieved by evaluating the integral deduced in 1953 by Demeur and incompletely calculated in 1969 by Jancovici, which I recover from Schwinger’s techniques of calculation. It yields [Formula: see text] with [Formula: see text] for [Formula: see text]. The [Formula: see text] truncation exceeds the precise estimate by 45% at [Formula: see text] and by more at lower values of [Formula: see text], due to neglecting, among others, the single logarithmic contribution. This is doubly unjustified because it is large and because it is needed to fulfill appropriate renormalization conditions. Technically challenging improvements look therefore necessary, for example, when resumming higher loops and incorporating the effects of large [Formula: see text] on the photonic vacuum polarization, like investigated in recent years.