Emergence of periodic in magnetic moment effective QED action

We evaluate for the inhomogeneous static electric Sauter step potential the imaginary part of the emerging homogeneous in electric field effective Euler-Heisenberg-Schwinger action sourced by vacuum fluctuations of a charged particle with magnetic moment of arbitrary strength. The result is convergent for all values of gyromagnetic ratio g, periodic in g, with a cusp at g = 2. We consider the relation to the QED beta-function which is also found to be periodic in g. We confirm presence of asymptotic freedom conditions using this novel method and document a wider range of g-values for which asymptotic freedom is present. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

In this study, we evaluate the imaginary part of the effective action in an electric field, sourced by vacuum fluctuations of a charged particle with magnetic moment. The result is found to be convergent for all values of the gyromagnetic ratio and exhibits periodicity, with a cusp at g = 2. We also examine the relationship to the QED beta-function, which shows periodic behavior in g. Using this novel method, we confirm the presence of asymptotic freedom conditions and identify a wider range of g-values for which asymptotic freedom is present.