Abstract
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a (relatively little known) Hamiltonian description of theories derived from second-order Lagrangians is presented. Unlike in the standard approach, the canonical momenta arising here are explicitly gauge-invariant and have a clear physical interpretation. The reduced symplectic form obtained this way is (almost) equivalent to Souriau's form. This approach illustrates a new method of deriving equations of motion from field equations.
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