Ukrainian mathematical congress - 2009

Anatoliy Prykarpatsky (Drohobych Ivan Franko State Pedagogical University, Ukraine)
Nikolai N. Bogolubov (Steklov Mathematical Institute RAS, Moscow, Russia)

A new vacuum field theory approach  to the Maxwell electrodynamics and the related lagrangian and hamiltonian analysis

The report is devoted to studying some new classical electro- dynamics models of interacting charged point particles and related with them the Maxwell-Lorentz and Einstein special relativity aspects. Based on the vacuum eld theory no- geometry approach, developed in [1, 2], the Lagrangian and Hamiltonian reformulations of some alternative classical elec- trodynamics models are devised. The Lorentz force structure and the Dirac type quantization procedure for the considered alternative electrodynamics models, based on the obtained canonical Hamiltonian formulations, are discussed.

[1] Bogolubov N.N. (jr.), Prykarpatsky A.K. The vacuum structure, special relativity and quantum mechanics revis- ited. Parts 1 and 2. Preprint ICTP, Trieste, IC/2008/091, IC/2008/051 (Available at: IC/2008/091)
[2] Prykarpatsky A.K., Bogolubov N.N. (Jr.) The Lagrangian and Hamiltonian formalisms for the classical relativis- tic electrodynamical models revisited. (arXiv:0810.3755v1 [gr-qc] 21 Oct 2008)