D. Chruscinski et J. Kijowski, EQUATIONS OF MOTION FROM FIELD-EQUATIONS AND A GAUGE-INVARIANT VARIATIONAL PRINCIPLE FOR THE MOTION OF CHARGED-PARTICLES, Journal of geometry and physics, 20(4), 1996, pp. 391-401
New, gauge-independent, second-order Lagrangian for the motion of clas
sical, charged test particles is proposed. It differs from the standar
d, gauge-dependent, first-order Lagrangian by boundary terms only. A n
ew method of deriving equations of motion from field equations is deve
loped. When applied to classical electrodynamics, this method enables
us to obtain unambiguously the above, second-order Lagrangian from the
general energy-momentum conservation principle.