A Cusp in QED at g=2

TL;DR

This paper investigates nonperturbative aspects of QED with arbitrary gyromagnetic ratio g, revealing a cusp in key coefficients and suggesting potential asymptotic freedom in an Abelian gauge theory for specific g values.

Contribution

It introduces a nonperturbative analysis of QED for g ≠ 2, identifying a cusp in the effective action and renormalization group coefficients, and explores conditions for asymptotic freedom.

Findings

Identifies a cusp in the effective action as a function of g.

Finds a cusp in the QED $b_0$-renormalization group coefficient.

Suggests the possibility of asymptotic freedom in Abelian theory for certain g domains.

Abstract

We explore nonperturbative properties of QED allowing a gyromagnetic ratio $g\ne g_{\rm D}\equiv 2$. 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 $g$.