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

Nikolai N. Bogolubov, Anatolij K. Prykarpatski and Denis Blackmore
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Nikolai N. Bogolubov: Mathematical Institute of RAS, Moscow, Russian Federation
Anatolij K. Prykarpatski: The Abdus Salam International Centre of Theoretical Physics, Trieste, Italy
Denis Blackmore: Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102-1982 USA

Mathematics, 2015, vol. 3, issue 2, 1-68

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.

Keywords: Ampère’s law; Lorentz force; Lorenz constraint; Maxwell electromagnetic equations; Lagrangian and Hamiltonian formalisms; radiation theory; vacuum field theory approach (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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