A Cusp in QED at g=2

Abstract

We explore nonperturbative properties of QED allowing a gyromagnetic ratio $g\ne g_{\mathrm{D}}\equiv 2$. We study the effective action $V_{\mathrm{eff}}$ for an arbitrarily strong constant and homogeneous field. Using the external field method, we find a cusp as a function of the gyromagnetic factor $g$ in: a) The QED $b_0$-renormalization group coefficient; b) A subclass of light-light scattering coefficients obtained in the long wavelength limit expansion. We recognize possibility of asymptotic freedom in an Abelian theory for certain domains of $g$.

Comments: 1+10+2 pages PTEP format: this "10th anniversary" v4 updates the contents, explains follow-up work (old update comments: v2 includes discussion of periodicity in g of Landau solutions v3 corects typos and adds explanations, v4 extends discussion adds recent developments and relation to experiment)