The Lagrangian and Hamiltonian formalisms for the classical relativistic electrodynamics models revisited

TL;DR

This paper revisits classical relativistic electrodynamics models, reformulating them using Lagrangian and Hamiltonian formalisms derived from vacuum field theory, and explores their quantization via the Dirac procedure.

Contribution

It introduces new Lagrangian and Hamiltonian formulations for alternative electrodynamics models based on vacuum field theory, and develops their quantization framework.

Findings

Canonical Hamiltonian formulations are obtained for the models.

A Dirac-type quantization procedure is developed.

The approach provides new insights into classical and quantum electrodynamics.

Abstract

The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in [6,7,9], the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained canonical Hamiltonian formulations, is developed.