A manifestly gauge-invariant Hamiltonian theory of the oscillation-centre dynamics

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Abstract
The theory of the slow reaction of charged particles in the presence of a high-frequency electromagnetic field (oscillation-centre motion) is developed by using a Hamiltonian formalism with non-canonical variables and pseudo-canonical transformations. The flexibility introduced by the latter features allows us to construct a theory which is manifestly gauge-invariant and involves only physical concepts (electromagnetic fields and particle velocities instead of potentials and canonical momenta). A complete description of the oscillation-centre dynamics is derived. The known expressions of the ponderomotive force are derived as special cases of our theory.