Abstract
The Hamiltonian formulation of relativistic system of charged particles plus electromagnetic field in the Dirac instant and front forms of dynamics is considered. The canonical realization of the Poincaré algebra in the terms of gauge-invariant variables is found. The procedure of elimination of the field degrees of freedom within the framework of the Dirac constraint theory is elaborated up to the first order in the coupling constant. The Poincaré generators in the terms of particle variables are obtained. The relations between the instant form generators and front form ones are examined. The instant form Hamiltonian in the weak-relativistic approximation results in the Darwin Hamiltonian.
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