The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079-1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.