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Mathematics 2015, 3(2), 190-257; doi:10.3390/math3020190

Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm

1
Mathematical Institute of RAS, Moscow, Russian Federation
2
The Abdus Salam International Centre of Theoretical Physics, Trieste, Italy
3
The Department of Applied Mathematics at AGH University of Science and Technology, Krakow 30059, Poland
4
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102-1982 USA
*
Author to whom correspondence should be addressed.
Academic Editor: Palle Jorgensen
Received: 25 January 2015 / Accepted: 27 March 2015 / Published: 17 April 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [498 KB, uploaded 21 April 2015]

Abstract

We review new electrodynamics models of interacting charged point particles and related fundamental physical aspects, motivated by the classical A.M. Ampère magnetic and H. Lorentz force laws electromagnetic field expressions. Based on the Feynman proper time paradigm and a recently devised vacuum field theory approach to the Lagrangian and Hamiltonian, the formulations of alternative classical electrodynamics models are analyzed in detail and their Dirac type quantization is suggested. Problems closely related to the radiation reaction force and electron mass inertia are analyzed. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis is argued. The related electromagnetic Dirac–Fock–Podolsky problem and symplectic properties of the Maxwell and Yang–Mills type dynamical systems are analyzed. The crucial importance of the remaining reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. View Full-Text
Keywords: Ampère’s law; Lorentz force; Lorenz constraint; Maxwell electromagnetic equations; Lagrangian and Hamiltonian formalisms; radiation theory; vacuum field theory approach Ampère’s law; Lorentz force; Lorenz constraint; Maxwell electromagnetic equations; Lagrangian and Hamiltonian formalisms; radiation theory; vacuum field theory approach
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Bogolubov, N.N., Jr.; Prykarpatski, A.K.; Blackmore, D. Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian Formalism and Feynman Proper Time Paradigm. Mathematics 2015, 3, 190-257.

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