Is there a Maximal Electrostatic Field Strength?

Abstract

Neglecting all nonelectromagnetic interactions, nonperturbative techniques are used based on an effective quantum-electrodynamic Lagrangian. A semiclassical argument leads to a finite classical electron radius ${\mathcal{r}}_{min}$ of the order of $\mathrm{exp}[\ensuremath{-}\frac{3\ensuremath{\pi}}{(2\ensuremath{\alpha})}]$ times the Compton wavelength, and to a corresponding maximal field strength ${E}_{max}\ensuremath{\sim}\frac{1}{{{\mathcal{r}}_{min}}^{2}}$ (in natural units). The charge renormalization constant ${Z}_{3}$ computed with the cutoff thus suggested consequently has a minimum value of $\frac{\ensuremath{\alpha}}{3}\ensuremath{\pi}$, corresponding to a finite bare charge. The bare mass is estimated to be of order ${\ensuremath{\alpha}}^{2}$ or possibly zero.