Study of QED singular properties for variable gyromagnetic ratio g similar or equal to 2

Using the external-field method, i.e., evaluating the effective action V-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 P-2n = ((E) over right arrow center dot (B) over right arrow)(2n) of light-light scattering coefficients. Properties of b(0) imply for certain domains of g asymptotic freedom in an Abelian theory.