### The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models

#### Abstract

The important classical Ampère’s and Lorentz laws derivations are revisited and their relationships with the modern vacuum field theory approach to modern relativistic electrodynamics are demonstrated. The relativistic models of the vacuum field medium and charged point particle dynamics as well as related classical electrodynamics problems jointly with the fundamental principles, characterizing the electrodynamical vacuum-field structure, based on the developed field theory concepts are reviewed and analyzed detail. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum field theory approach. There are obtained the main classical special relativity theory relationships and their new explanations. The well known Feynman approach to Maxwell electromagnetic equations and the Lorentz type force derivation is also. A related charged point particle dynamics and a hadronic string model analysis is also presented. We also revisited and reanalyzed the classical Lorentz force expression in arbitrary non-inertial reference frames and present some new interpretations of the relations between special relativity theory and its quantum mechanical aspects. Some results related with the charge particle radiation problem and the magnetic potential topological aspects are discussed. The electromagnetic Dirac-Fock-Podolsky problem of the Maxwell and Yang-Mills type dynamical systems is analyzed within the classical Dirac-Marsden-Weinstein symplectic reduction theory. Based on the Gelfand-Vilenkin representation theory of infinite dimensional groups and the Goldin-Menikoff-Sharp theory of generating Bogolubov type functionals the problem of constructing Fock type representations and retrieving their creation-annihilation operator structure is analyzed. An application of the suitable current algebra representation to describing the non-relativistic Aharonov-Bohm paradox is demonstrated. The current algebra coherent functional representations are constructed and their importance subject to the linearization problem of nonlinear dynamical systems in Hilbert spaces is also presented.

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