A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics

Abstract

A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics is constructed by taking the electromagnetic fields as the basic dynamical quantities, obeying appropriate Lie-bracket relations. The longitudinal parts of the fields can be eliminated completely from the beginning. The theory is relativistically covariant: the generators of the Poincaré Lie algebra are given explicitly. Explicit realizations of the Lie-bracket operation are derived (they are different from the usual Poisson brackets), and the relativistic Liouville equations are presented.