Strong-field QED in Furry-picture momentum-space formulation: Ward identities and Feynman diagrams

TL;DR

This paper develops a momentum-space formulation of strong-field QED in the Furry picture, clarifying Ward identities and Feynman diagrams, and demonstrating its advantages over position-space approaches for modeling laser pulse interactions.

Contribution

It introduces a systematic momentum-space approach to strong-field QED that simplifies the treatment of Ward identities and Feynman diagrams in the presence of finite-duration background fields.

Findings

Systematic momentum-space formulation of strong-field QED.

Recovery of standard perturbative QED in the weak-field limit.

Application examples demonstrating Feynman rules and vertex functions.

Abstract

The impact of a strong electromagnetic background field on otherwise perturbative QED processes is studied in the momentum-space formulation. The univariate background field is assumed to have finite support in time, thus being suitable to provide a model for a strong laser pulse in plane-wave approximation. The usually employed Furry picture in position space must be equipped with some non-obvious terms to ensure the Ward identity. In contrast, the momentum space formulation allows for an easy and systematic account of these terms, both globally and order-by-order in the weak-field expansion. In the limit of an infinitely long-acting (monochromatic) background field, these terms become gradually suppressed, and the standard perturbative QED Feynman diagrams are recovered in the leading-order weak-field limit. A few examples of three- and four-point amplitudes are considered to demonstrate the application of our Feynman rules which employ free Dirac spinors, the free photon propagator, and the free Fermion propagator, while the external field impact is solely encoded in the Fermion-Fermion-photon vertex function. The appearance of on-/off-shell contributions, singular structures, and Oleinik resonances is pointed out.