Gauge-invariant formulation of the electromagnetic interaction in Hamiltonian mechanics

Abstract

Making use of the fact that for an arbitrary autonomous mechanical system any constant of motion can be used as Hamiltonian, the equations of motion of a charged particle in an electromagnetic field are written in Hamiltonian form without introducing potentials for the electromagnetic field. It is shown that the Hamiltonian and the Poisson bracket obtained here coincide with those appearing in the standard Hamiltonian formulation.