Everlasting interaction: polarization summation without a Landau pole

Abstract

We propose an external field approach to evaluating effective action allowing the interaction to act everywhere at all times (everlasting). Requiring that the asymptotic gauge fields are always-interacting, we implement displacement fields encoding polarization corrections into the derivation of effective action. The result is a novel polarization summation for one-cut reducible loop diagrams, which can be applied to two cases: transient quasi-constant electromagnetic fields, and everlasting interactions. In the first case, a perturbative expansion of our result recovers the Schwinger-Dyson reducible diagram series with a Landau pole. The everlasting summation evaluated in nonperturbative fashion removes the Landau pole, providing a new avenue for modeling strongly interacting theories.

7 pages, discussion of prior work relegated to separate comment [arXiv:2403.09745]