  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.
