Tadpole diagrams in constant electromagnetic fields

TL;DR

This paper develops an algebraic method to construct all tadpole diagrams in constant electromagnetic fields from irreducible diagrams, enabling systematic calculations of quantum corrections in such backgrounds.

Contribution

It introduces a novel algebraic approach to derive tadpole diagrams from irreducible diagrams in constant fields, including new two-loop and one-loop corrections.

Findings

Derived tadpole contributions to the two-loop photon polarization tensor.

Presented a new one-loop correction to charged particle propagators.

Established a systematic construction method for diagrams in constant electromagnetic fields.

Abstract

We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations of the latter class of diagrams with respect to the field strength tensor and contractions with derivatives of the one-particle irreducible part of the Heisenberg-Euler effective Lagrangian in constant fields. Specific examples include the two-loop addendum to the Heisenberg-Euler effective action as well as a novel one-loop correction to the charged particle propagator in constant electromagnetic fields discovered recently. As an additional example, the approach devised in the present article is adopted to derive the tadpole contribution to the two-loop photon polarization tensor in constant fields for the first time.