Dirac's hamiltonian formalism and gauge-invariant classical electrodynamics

Using Dirac's method of constraints we study the problem of a gauge-invariant hamiltonian formulation of a relativistic plasma. In particular we get a hamiltonian formulation strictly in terms of the electric and magnetic fields, and the mechanical momenta of the particles. The explicit Lie-bracket relations between the fundamental microscopic variables is no longer canonical. These Lie-bracket relations and the equations of motion are given by Dirac's modified Poisson bracket.