## 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.

Original language | English (US) |
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Pages (from-to) | 190-257 |

Number of pages | 68 |

Journal | Mathematics |

Volume | 3 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2015 |

## All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)

## Keywords

- Ampère's law
- Lagrangian and Hamiltonian formalisms
- Lorentz force
- Lorenz constraint
- Maxwell electromagnetic equations
- Radiation theory
- Vacuum field theory approach