Abstract
A consistent relativistic theory of the classical Maxwell field interacting with classical, charged, point-like particles, proposed in [1], is now derived from a variational principle. For this purpose a new electrodynamical Lagrangian based on fluxes is constructed. As a result, we obtain the action principle where i) field degrees of freedom and particle degrees of freedom are kept at the same footing, ii) contrary to the standard formulation, no infinities arise, iii) energy (Hamiltonian) is obtained from the Lagrangian via the Legendre transformation, without any need of “adding a complete divergence”.
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Kijowski, J., Chruściński, D. Variational principle for electrodynamics of moving particles. Gen Relat Gravit 27, 267–311 (1995). https://doi.org/10.1007/BF02109126
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DOI: https://doi.org/10.1007/BF02109126