One-particle reducible contribution to the one-loop scalar propagator in a constant field

TL;DR

This paper reveals a previously overlooked one-particle reducible contribution to the one-loop scalar propagator in a constant field, extending the understanding of quantum corrections in scalar QED and related theories.

Contribution

It demonstrates the existence of a one-particle reducible contribution at one-loop level for the scalar propagator in a constant field and provides a unified derivation using the worldline formalism.

Findings

Identifies a one-particle reducible contribution at one-loop in scalar QED.

Provides a new derivation of Gies-Karbstein results using worldline formalism.

Enhances the understanding of quantum corrections in constant electromagnetic fields.

Abstract

Recently, Gies and Karbstein showed that the two-loop Euler-Heisenberg Lagrangian receives a finite one-particle reducible contribution in addition to the well-known one-particle irreducible one. Here, we demonstrate that a similar contribution exists for the propagator in a constant field already at the one-loop level, and we calculate this contribution for the scalar QED case. We also present an independent derivation of the Gies-Karbstein result using the worldline formalism, treating the scalar and spinor QED cases in a unified manner.