Study of QED singular properties for variable gyromagnetic ratio $g\simeq 2$

Abstract

Using the external field method, {\it 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 ${\mathcal{P}}^{2n}=(\vec{E}\cdot \vec{B}{)}^{2n}$ of light-light scattering coefficients. Properties of $b_0$ imply for certain domains of $g$ asymptotic freedom in an Abelian theory.

Comments: 12 pages, 3 figures. This paper builds on the work in arXiv:1205.1835, motivated by recent advances in the Dirac-Pauli-based QED effective action, and with extended author list