Closed-form solution for elliptical-polarization BMT spin dynamics

Derive a closed-form solution of the Bargmann–Michel–Telegdi spin equation for an electron interacting with an elliptically polarized plane-wave field at g2 beyond the constant-modulus polarization profile.

Background

The paper establishes an exact algebraic solution for the electron orbit and spin evolution in a linearly polarized plane-wave pulse. In that case, the anomalous-moment rotation occurs about a fixed axis, so rotations at different light-front phases commute and the spin evolution can be written in closed form.

For elliptical polarization with g2, the anomalous-precession axis changes with the transverse vector potential. The resulting rotations at different phases generally do not commute, and the paper treats this regime numerically using a physics-informed neural network. A closed form is identified only for the constant-modulus profile, leaving the general elliptically polarized case unresolved.

References

For elliptical polarization at $g\neq2$ no closed-form solution is known beyond the constant-modulus profile, and the net rotation after the pulse is a holonomy of second order in the anomaly.

— Rapidity-Coupled Spin Dynamics in Pulsed Laser Fields from Physics-Informed Neural Networks  (2609.19756 - Akintsov et al., 17 Sep 2026) in Introduction, first paragraph; see also Section S1, subsection “Elliptical polarization”