Abstract
Using the external-field method, i.e., evaluating the effective action ${V}_{\mathrm{eff}}$ for an arbitrarily strong constant and homogeneous field, we explore nonperturbative properties of QED allowing arbitrary gyromagnetic ratio $g$. We find a cusp at $g=2$ in (a) The QED ${b}_{0}$-renormalization group coefficient, and in the infinite-wavelength limit in (b) a subclass containing the pseudoscalar ${\mathcal{P}}^{2n}=(\stackrel{\ensuremath{\rightarrow}}{E}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{B}{)}^{2n}$ of light-light scattering coefficients. Properties of ${b}_{0}$ imply for certain domains of $g$ asymptotic freedom in an Abelian theory.
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