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

## TL;DR

This paper extends the understanding of one-particle reducible contributions to the one-loop spinor propagator in a constant electromagnetic field, using a novel worldline path integral approach, revealing similar relations as in the scalar case.

## Contribution

It generalizes the reducible contribution findings from scalar to spinor particles, employing a new worldline path integral representation.

## Key findings

- Identifies the reducible contribution for spinor propagators in a constant field.
- Establishes the relation between reducible term, tree-level propagator, and Euler-Heisenberg Lagrangian.
- Introduces a novel worldline path integral method for spinor propagators.

## Abstract

Extending work by Gies and Karbstein on the Euler-Heisenberg Lagrangian, it has recently been shown that the one-loop propagator of a charged scalar particle in a constant electromagnetic field has a one-particle reducible contribution in addition to the well-studied irreducible one. Here we further generalize this result to the spinor case, and find the same relation between the reducible term, the tree-level propagator and the one-loop Euler-Heisenberg Lagrangian as in the scalar case. Our demonstration uses a novel worldline path integral representation of the photon-dressed spinor propagator in a constant electromagnetic field background.