The work is devoted to the study of the Lagrangian and Hamiltonian properties of some relativistic electrodynamics models and is a continuation of our previous investigations. Based on the vacuum field theory approach, the Lagrangian and Hamiltonian reformulation of some classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed. Within the approach proposed in the work a possibility of the combined description both of electrodynamics and gravity is analyzed.

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