Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field

TL;DR

This paper develops a relativistic ponderomotive Hamiltonian for a Dirac electron in a high-frequency laser field, capturing spin dynamics, ponderomotive forces, and background interactions, useful for relativistic spin-$1/2$ plasma studies.

Contribution

It derives a reduced phase-space Lagrangian from the Dirac Lagrangian, incorporating spin effects and large-amplitude laser fields in vacuum, extending previous models.

Findings

Agreement with BMT spin precession shown numerically

Reproduces conventional ponderomotive effects as a special case

Model applicable to relativistic spin-$1/2$ plasma interactions

Abstract

We report a point-particle ponderomotive model of a Dirac electron oscillating in a high-frequency field. Starting from the Dirac Lagrangian density, we derive a reduced phase-space Lagrangian that describes the relativistic time-averaged dynamics of such a particle in a geometrical-optics laser pulse propagating in vacuum. The pulse is allowed to have an arbitrarily large amplitude (provided radiation damping and pair production are negligible) and a wavelength comparable to the particle de Broglie wavelength. The model captures the Bargmann-Michel-Telegdi (BMT) spin dynamics, the Stern-Gerlach spin-orbital coupling, the conventional ponderomotive forces, and the interaction with large-scale background fields. Agreement with the BMT spin precesison equation is shown numerically. The commonly known theory in which ponderomotive effects are incorporated in the particle effective mass is reproduced as a special case when the spin-orbital coupling is negligible. This model could be useful for studying laser-plasma interactions in relativistic spin-$1/2$ plasmas.