Universal Journal of Physics and Application Vol. 7(2), pp. 160 - 178
DOI: 10.13189/ujpa.2013.010216
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Mathematical Foundations of the Classical Maxwell-Lorentz Electrodynamic Models in the Canonical Lagrangian and Hamiltonian Formalisms

Denis Blackmore^1,*, Anatolij K. Prykarpatski², Nikolai N. Bogolubov (Jr.)³, Jan J. S lawianowski^3
1 Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102-1982 USA
² Department of Applied Mathematics at AGH University of Science and Technology, Krakow 30059, Poland
³ V.A. Steklov Mathematical Institute of RAS, Moscow Russian Federation and the Abdus Salam International Centre of Theoretical Physics, Trieste, Italy

ABSTRACT

We present new mathematical foundations of classical Maxwell–Lorentz electrodynamic models and related charged particles interaction-radiation problems, and analyze the fundamental least action principles via canonical Lagrangian and Hamiltonian formalisms. The corresponding electrodynamic vacuum field theory aspects of the classical Maxwell–Lorentz theory are analyzed in detail. Electrodynamic models of charged point particle dynamics based on a Maxwell type vacuum field medium description are described, and new field theory concepts related to the mass particle paradigms are discussed. We also revisit and reanalyze the mathematical structure of the classical Lorentz force expression with respect to arbitrary inertial reference frames and present new interpretations of some classical special relativity theory relationships.

KEYWORDS
Lagrangian and Hamiltonian Formalism, Least Action Principle, Vacuum Field Theory, Lorentz Force Problem, Feynman Approach, Maxwell Equations, Lorentz Constraint, Electron Radiation Theory

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Denis Blackmore , Anatolij K. Prykarpatski , Nikolai N. Bogolubov (Jr.) , Jan J. S lawianowski , "Mathematical Foundations of the Classical Maxwell-Lorentz Electrodynamic Models in the Canonical Lagrangian and Hamiltonian Formalisms," Universal Journal of Physics and Application, Vol. 7, No. 2, pp. 160 - 178, 2013. DOI: 10.13189/ujpa.2013.010216.

(b). APA Format:
Denis Blackmore , Anatolij K. Prykarpatski , Nikolai N. Bogolubov (Jr.) , Jan J. S lawianowski (2013). Mathematical Foundations of the Classical Maxwell-Lorentz Electrodynamic Models in the Canonical Lagrangian and Hamiltonian Formalisms. Universal Journal of Physics and Application, 7(2), 160 - 178. DOI: 10.13189/ujpa.2013.010216.