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  • Open Access

Scattering in strong field QED in a nonnull background

Patrick Copinger1,2,*, James P. Edwards2,†, and Karthik Rajeev3,‡

  • 1International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8531, Japan
  • 2Centre for Mathematical Sciences, University of Plymouth, Plymouth PL4 8AA, United Kingdom
  • 3Higgs Centre, School of Physics and Astronomy, University of Edinburgh, EH9 3FD, United Kingdom

  • *Contact author: copinger@hiroshima-u.ac.jp
  • †Contact author: james.p.edwards@plymouth.ac.uk
  • ‡Contact author: karthik.rajeev@ed.ac.uk
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Phys. Rev. D 114, 016015 – Published 16 July, 2026

DOI: https://doi.org/10.1103/ggn1-3mnm

Abstract

We examine scattering amplitudes for an arbitrary number of photons in a class of nonnull background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by a gauge field Aμ(n·x) for n2≠0. Motivated to account for more physically realistic laser-plasma dispersive properties, our approach overcomes prior work studying such amplitudes in a constant background field and relaxes the familiar null criterion assumed for plane waves. Master formulas for the N-photon amplitudes dressed by the nonnull background are constructed using the first-quantized worldline formalism, which can systematically account for all orders in the nonnull parameter, n2, treated here as an expansion parameter. These are derived from worldline representations of the coordinate and momentum space propagators (and their LSZ-truncated amplitudes) and the effective action, each incorporating the nonnull background nonperturbatively. We then outline a partial resummation of their expansions in n2. A special exactly solvable case of nonnull constant crossed fields without photon insertion in the effective action is explored to test the master formulas that result. The validity of the presented master formulas is further checked against known expressions for the wave function and nonlinear Compton scattering in a nonnull background to lowest order in the nonnull parameter.

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Phys. Rev. D 114, 016015– Published 16 July, 2026
  • Received 14 May 2026
  • Accepted 15 June 2026
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