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Nonlinear trident using WKB and worldline instantons

Gianluca Degli Esposti1,2,* and Greger Torgrimsson3,†

  • *Contact author: g.degli-esposti@hzdr.de
  • †Contact author: greger.torgrimsson@umu.se
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Phys. Rev. D 112, 036005 – Published 11 August, 2025

DOI: https://doi.org/10.1103/vpyq-qs23

Abstract

We consider nonlinear trident, e−→e−e−e+, in various electric background fields. This process has so far been studied for plane-wave backgrounds, using Volkov solutions. Here we first use WKB for trident in time-dependent electric fields, and then for fields which vary slowly in space. Then we show how to use worldline instantons for more general fields which depend on both time and space. For time-dependent fields the WKB approach is at least as simple to use as the worldline approach, but already the relatively modest step of including a slow spatial dependence makes the worldline approach much more efficient.

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Phys. Rev. D 112, 036005– Published 11 August, 2025
  • Received 30 March 2025
  • Accepted 22 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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