2009
DOI: 10.1007/s10701-009-9399-1
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The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

Abstract: 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… Show more

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Cited by 14 publications
(48 citation statements)
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“…As for the general case of (3.1) results analogous to the above results hold, as described in detail in [15][16][17][18]. We need only mention that the Hamiltonian structure of the general equation (3.1) results naturally from its least action representation (3.7) with respect to the rest reference frame K(τ, q).…”
Section: Corollary 34supporting
confidence: 60%
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“…As for the general case of (3.1) results analogous to the above results hold, as described in detail in [15][16][17][18]. We need only mention that the Hamiltonian structure of the general equation (3.1) results naturally from its least action representation (3.7) with respect to the rest reference frame K(τ, q).…”
Section: Corollary 34supporting
confidence: 60%
“…His result was analyzed by many authors [3-9, 11, 24] from different points of view, including its relativistic generalization [10]. As this problem is completely classical, we reanalyze the Feynman's derivation from the classical Hamiltonian dynamics point of view on the coadjoint space T * (N ), N ⊂ R 3 , and construct its nontrivial generalization compatible with results [15,16] of Sect. 1, based on a recently devised vacuum field theory approach [15,18].…”
Section: Introductionmentioning
confidence: 91%
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“…It is well known [5,3,9,12,13,11] that the Hamiltonian formulation of Maxwell's electromagnetic field equations involves a very important classical problem; namely, to intrinsically introduce the Lorentz condition, which guarantees the wave structure of propagating quanta and the positivity of energy. Unfortunately, in spite of extensive classical studies by Dirac, Fock and Podolsky [10], the problem remains open.…”
Section: Introductionmentioning
confidence: 99%