Study of QED singular properties for variable gyromagnetic ratio g≃2

Using the external-field method, i.e., evaluating the effective action Veff 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 b0-renormalization group coefficient, and in the infinite-wavelength limit in (b) a subclass containing the pseudoscalar P2n=(E→·B→)2n of light-light scattering coefficients. Properties of b0 imply for certain domains of g asymptotic freedom in an Abelian theory.