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The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
Magnetically uncharged, magnetic linear response of the vacuum filled with arbitrarily combined constant electric and magnetic fields to an imposed static electric charge is found within general nonlinear electrodynamics. When the electric…
The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The…
The quantum-mechanical solution to the problem of radiative recombination of an electron in a Coulomb field, obtained in the approximation of the smallness of the electron coupling with the radiation field, has been known for a long time.…
Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron oscillation through the nuclei of H2+ accounts for…
Recently it was shown that classical "relativistic" particle dynamics was implicit in physics going back to Maxwell. The demonstration utilized a simple modification of a 1906 thought experiment by which Einstein established the mass…
The possibility of the effect of electromagnetic radiation (hereinafter - radiation from vacuum) due to the interaction of zero-point vacuum fluctuations with free charged particles accelerated at relativistic speeds in electric or magnetic…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell…
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the formal Bohr's correspondence principle of…
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b)…
We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb's law at $r\rightarrow\infty$ are obtained and energy…
The intrinsic covariant 1-time description (rest-frame instant form) for N relativistic scalar particles is defined. The system of N charged scalar particles plus the electromagnetic field is described in this way: the study of its Dirac…
The main notions of semiclassical scalar electrodynamics in different gauges (Hamiltonian, Couloumb, Lorentz) are discussed. These are semiclassical states, Poincare transformations, fields, observables, gauge equivalence. General…
The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this article, we explain the reason behind this…
A fully consistent classical relativistic electrodynamics with spinless point charges is constructed. The classical evolution of the electromagnetic fields is governed by the nonlinear Maxwell--Born--Infeld field equations, the classical…
In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…