Elimination of the field degrees of freedom in relativistic system of pointlike charges (Q2783456)

The object of study is a relativistic system of \(N\) charged particles in the electromagnetic field of four-potential \(A_\mu(x)\), where \(x\in \mathbb{M}_4=\) the Minkowskian spacetime. Following Dirac's theory, the problem is to eliminate the field constrained, and to describe the system in terms of particle variables. The procedure is usually based on some formal solution of the field equations, which modifies the action integral and the resulting Hamiltonian description. Alternatively, in this paper, it is shown that the elimination of the field degrees of freedom is possible after the transition to the Hamiltonian description. This method is then applied to the system in the front form dynamics, where it allows the study of the corresponding generators.