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Classical and quantum double copy of back-reaction

Tim Adamo, Anton Ilderton

TL;DR

The authors address back-reaction from radiation by colour-charged and massive particles traversing strong plane-wave backgrounds in YM and gravity, treating the backgrounds exactly and non-perturbatively. They compare the classical worldline results with tree-level quantum three-point amplitudes, establishing their consistency and showing that the gravity amplitudes are related to gauge-theory amplitudes by a plane-wave version of the double copy. A key advance is the demonstration that, in four dimensions, a background-dressed spinor-helicity formalism can elegantly encode dressed momenta and polarizations, simplifying the non-linear Compton amplitudes for both gluon and graviton emission. The work provides both a classical and quantum understanding of back-reaction in strong-field backgrounds and demonstrates that the double-copy relation persists beyond trivial spacetime. These results broaden the scope of double copy to nontrivial backgrounds and offer practical tools for exact calculations in strong-field QFT and gravitational radiation contexts.

Abstract

We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism.

Classical and quantum double copy of back-reaction

TL;DR

The authors address back-reaction from radiation by colour-charged and massive particles traversing strong plane-wave backgrounds in YM and gravity, treating the backgrounds exactly and non-perturbatively. They compare the classical worldline results with tree-level quantum three-point amplitudes, establishing their consistency and showing that the gravity amplitudes are related to gauge-theory amplitudes by a plane-wave version of the double copy. A key advance is the demonstration that, in four dimensions, a background-dressed spinor-helicity formalism can elegantly encode dressed momenta and polarizations, simplifying the non-linear Compton amplitudes for both gluon and graviton emission. The work provides both a classical and quantum understanding of back-reaction in strong-field backgrounds and demonstrates that the double-copy relation persists beyond trivial spacetime. These results broaden the scope of double copy to nontrivial backgrounds and offer practical tools for exact calculations in strong-field QFT and gravitational radiation contexts.

Abstract

We consider radiation emitted by colour-charged and massive particles crossing strong plane wave backgrounds in gauge theory and gravity. These backgrounds are treated exactly and non-perturbatively throughout. We compute the back-reaction on these fields from the radiation emitted by the probe particles: classically through background-coupled worldline theories, and at tree-level in the quantum theory through three-point amplitudes. Consistency of these two methods is established explicitly. We show that the gauge theory and gravity amplitudes are related by the double copy for amplitudes on plane wave backgrounds. Finally, we demonstrate that in four-dimensions these calculations can be carried out with a background-dressed version of the massive spinor-helicity formalism.

Paper Structure

This paper contains 16 sections, 139 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Plane wave backgrounds
  3. Classical colour charge dynamics
  4. Zeroth order: charge motion in the background
  5. First order: emission and back-reaction
  6. Classical gravitational mass dynamics
  7. Zeroth order: particle motion in the background
  8. First order: emission and back-reaction
  9. Non-linear Compton scattering
  10. Gluon emission amplitude
  11. Graviton emission amplitude
  12. Double copy
  13. Four-dimensions and spinor helicity
  14. The formalism
  15. 4d non-linear Compton amplitudes
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Tree-level non-linear Compton scattering on a plane wave background. Double lines indicate that the particles are fully dressed by the plane wave: in vacuum, the corresponding amplitudes would vanish by momentum conservation, but here they are nontrivial functions of the scattering momenta and the background.