A gauge-invariant Hamiltonian description of the motion of charged test particles (Q1299226)

In an earlier paper [ibid. 20, No. 4, 393-403 (1996; Zbl 0869.70010)], the authors have shown that the motion of charged test particles in an electromagnetic field can be derived from a gauge-invariant second-order Lagrangian which differs from the (gauge-dependent first-order) standard Lagrangian by a boundary term. The paper under review is devoted to the corresponding Hamiltonian theory. A characteristic feature of this approach is that, unlike in the standard formulation, the canonical momenta are gauge-invariant and have a clear physical meaning. The particle trajectories are constructed as the characteristic curves of a pre-symplectic form \(\Omega_N\) on the evolution space; this form \(\Omega_N\) is uniquely determined by the gauge-invariant Lagrangian via the Legendre transformation.