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  • Open Access

Scattering and depletion in a flying focus from conformal transformations

Tim Adamo1,*, Anton Ilderton2,†, and Adam Noble3,‡

  • *Contact author: t.adamo@ed.ac.uk
  • †Contact author: anton.ilderton@ed.ac.uk
  • ‡Contact author: adam.noble@strath.ac.uk
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Phys. Rev. D 114, 056022 – Published 22 September, 2026

DOI: https://doi.org/10.1103/b3gf-ls99

Abstract

We show that flying-focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying-focus beam may be computed directly from the corresponding plane-wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focusing effects into strong-field QED calculations “for free.” The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.

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Phys. Rev. D 114, 056022– Published 22 September, 2026
  • Received 25 May 2026
  • Accepted 3 September 2026
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