On the Classical Maxwell–Lorentz Electrodynamics, the Electron Inertia Problem, and the Feynman Proper Time Paradigm

Abstract

The Maxwell electromagnetic and the Lorentz type force equations are derived in the framework of the R. Feynman proper time paradigm and the related vacuum field theory approach. The electron inertia problem is analyzed within the Lagrangian and Hamiltonian formalisms and the related pressure-energy compensation principle. The modified Abraham-Lorentz damping radiation force is derived, the electromagnetic elctron mass origin is argued.

The Quantum Fermionic Charged Particle Self-Interaction Problem within the Fock Multitime and Feynman Proper Time Paradigms

“…The latter are completely non-relativistic and based on the canonical quantization scheme [7,71] in the case of the Coulomb gauge condition. Inspired by these and related classical results, we have shown that the quantum mechanism of self-interaction of a charged particle with its self-generated electromagnetic field consists of two physically different phenomena, whose influence on the structure of the resulting Hamilton interaction operator appears to be crucial and gives rise [64] to a modified analysis of the related classical shell model of a charged particle within the Lagrangian formalism. As a result of our scrutiny of studying the classical electromagnetic mass problem, there was demonstrated that it can be satisfactorily solved within the classical H. Lorentz and M. Abraham arguments augmented with the additional electron stability condition, which was not taken before into account yet and appeared to be very important for balancing the related electromagnetic field and mechanical electron momenta.…”

“…As was shown in [64], the consequences formulated above subject to the quantum fermionic-bosonic selfinteracting phenomenon appear to be very important from the classical point of view, especially for the physical comprehension of the inertial properties of a charged particle under the action of the self-generated electromagnetic field.…”

“…governing the temporal evolution of the charged particle and the electromagnetic field with respect to the laboratory reference frame . The above-obtained Hamiltonian function and its corresponding Lagrangian form (16) have been effectively used before in [64] to describe the classical selfinteracting charged particle dynamics and its inertial properties.…”

“…acting in the Fock spaceΦ suitably transformed and reduced by means of the operator Lorentz-type constraint (48) with respect to the common reference frame . The very complicated quantum spectral problem (70) was recently analyzed in [64] from the classical point of view in detail. A thorough analytical study of the mass expression (70) is under elaboration.…”

On the electron spin and spectrum energy problems within the Fock many temporal and Feynman proper time paradigms

“…for all k ∈ E 3 , contradicting the relationships, following from the evolution equations (38). As the latter relationships should be vanishing in the Fock space, it was suggested [12] to reduce the Fock space Φ to a subspace, on which there are satisfied the weak operator constraints (41).…”