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

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

2012-04-16

arxiv.org/abs/1204.5129v1

Physics

Mathematical Physics

63 p

Scientific paper

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuumfield structure. We analyze the models of the vacuumfield medium and charged point particle dynamics using the developed field theory concepts. 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. In particular, there are obtained the main classical special relativity theory relations and their new explanations. The well known Feynman approach to Maxwell electromagnetic equations and the Lorentz type force derivation is also discussed in detail. 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 an effective approach to study dynamical systems in Hilbert spaces is reviewed. An application of the suitable current algebra representation to describing the non-relativistic Aharonov-Bohm paradox is presented.

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