# Reducible contributions to quantum electrodynamics in external fields

## TL;DR

This paper investigates one-particle reducible contributions in quantum electrodynamics within external fields, revealing that these contributions are either divergences or physical corrections depending on the field type, with exact calculations provided.

## Contribution

It provides the first detailed analysis of 1PR contributions in various external fields at one- and two-loop orders, including exact and approximate results.

## Key findings

- 1PR tadpoles are non-zero in plane waves and crossed fields, contributing only divergences.
- In magnetic fields, 1PR tadpoles yield physical corrections to QED processes.
- The study offers exact solutions and weak/strong field expansions for magnetic fields.

## Abstract

We consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one-loop and two-loop order. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one-loop and beyond. Our calculations are exact in the external fields and we give strong and weak field expansions in the magnetic case.