Scientists have derived equations describing how a charged particle that also spins slows down when it emits light, extending the classic Abraham–Lorentz–Dirac formula to include spin up to second order. The researchers calculated the particle’s own electromagnetic field on its trajectory and used dimensional regularisation to remove infinities, a method traced back to Sidney Coleman.

Using the new equations, they computed the light pattern produced when the spinning body scatters off a stationary charge. The result matches exactly the prediction from a quantum‑field‑theory calculation that builds the same light pattern from scattering amplitudes, confirming both approaches agree through quadratic spin order.

Both methods recover known results for linear‑in‑spin self‑force effects and for the spinless case in six dimensions, offering a stringent cross‑check. The amplitude‑based calculation could in principle be pushed to higher spin, but is limited to spin‑squared order because of pesky poles in the classical Compton amplitudes.

The derived equations contain higher‑time derivatives, which can lead to runaway or premature acceleration. A standard remedy—reducing the equation order to the Landau–Lifshitz form—removes these unphysical solutions.

Finally, the work points out that extending the analysis to odd spacetime dimensions is not straightforward, since the light‑cone support of the retarded Green’s function changes and introduces logarithmic divergences.

The imaginary part of the one‑loop waveform, the key observable, is isolated via a double‑cut of the internal messenger propagator and the spinning line, providing a direct amplitude route to radiation reaction.