Nonperturbative Aspects in the QED Vacuum Related to Anomalous Magnetic Moment

Abstract

We study nonperturbative aspects of the QED vacuum response to electromagnetic fields. In sufficiently strong, very slowly varying (on the Compton wavelength scale) electromagnetic fields, the vacuum acquires properties of a nonlinear dielectric. The collective action of an infinite number of infrared photons leads to possible spontaneous decay into particle-antiparticle pairs. Our focus is the role of the anomalous magnetic moment, as it is applied to generalize the QED action for spin-$1/2$ particles to include values of gyromagnetic ratio $g\ne 2$. Efforts to incorporate $g\ne 2$ into the QED action span over 50 years, initially based on the Schwinger (1951) proper time formulation for $|g|\leq2$. We generalize the $|g|\leq2$ Euler-Heisenberg-Schwinger result and the effective action for a static finite Sauter potential step. In order to obtain a convergent effective action in the domain $|g|>2$ previously not accessible from the proper time method, we apply the following methods in computation of QED effective action: The Weisskopf (1936) Landau energy summation and the Nikishov (1969) Bogoliubov coefficient summation. We find a periodic in magnetic moment effective action and beta-function, with singular properties uncovered at the electron's (tree-level) gyromagnetic ratio $g=2$, and domains of $g$ far from 2 for which asymptotic freedom is present. Considered as a function of $g$, the cusp at $g=2$ in the beta-function and in the effective action, with nonperturbative dependence on the pseudoscalar $\mathcal{E}\cdot\mathcal{B}$, are among the significant results of this thesis. While perturbative QED for weak fields is well understood, our nonperturbative results could lead, in magnetically dominated fields, to new phenomena beyond the Schwinger critical field scale. Our anomalous magnetic moment study provides radiative corrections that impact particle production in fields with $\mathcal{E}\cdot\mathcal{B}$ present. Incorporating the measured $g_{\mathrm{electron}}$ amounts to the sum of vertex corrections to infinite irreducible loop order. This resummation produces a drastic suppression of the particle production rate. We show how convergence of expansion in fine structure $\alpha=1/137$ of this result depends on the strength of the $\mathcal{B}$ field. This feature is of interest in the context of strong (EM) fields relevant to magnetars and non-relativistic heavy-ion collisions. Moreover, in such environments, mass and magnetic moment become field-dependent quantities. As first steps toward improving understanding of how mass and $g$ respond to strong fields, we explore a classical self-consistent formulation of mass modification in external fields. Some of the nonperturbative in $g$ phenomena in strong field QED environments are analogous to properties of strong interactions. We consider how EM fields with pseudoscalar $\mathcal{E}\cdot\mathcal{B}$, which are suitable for probing $g$ effects in QED, can also probe effects outside of QED. As a first step in this direction, we developed the contribution to action from virtual axion-like particle excitations. For $g=2$, we demonstrate cases where these excitations may surpass the electron loop Euler-Heisenberg effect. This provides a potentially observable signal in probes of vacuum birefringence under development today.