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The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
We present a theoretical technique for solving the quantum transport problem of a few photons through a one-dimensional, strongly nonlinear waveguide. We specifically consider the situation where the evolution of the optical field is…
Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but…
It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive…
Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…
We study a general problem of the translational/rotational/vibrational/electronic dynamics of a diatomic molecule exposed to an interaction with an arbitrary external electromagnetic field. The theory developed in this paper is relevant to…
Maxwell Electrodynamics can be described either in Minkowski space-time or in a dynamically equivalent way in a curved geometry constructed in terms of the electromagnetic field. For this the field must have a superior bound limited by a…
Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas. However, exact local energy-momentum conservation law for the electromagnetic gyrokinetic system has not been found…
The Galilean symmetry and the Poincare symmetry are usually taken as the fundamental (relativity) symmetries for `nonrelativistic' and `relativistic' physics, respectively, quantum or classical. Our fully group theoretical formulation…
We study the contributions of off-resonant transitions to the dynamics of a system of N multilevel atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The Rotating Wave Approximation significantly…
A generalized approach of the Born-Oppenheimer approximation is developed to analytically deal with the influence exercised by the spatial motion of atom's mass-center on a two-level atom in an optical ring cavity with a quantized…
In a recent Foundations of Physics paper [5] by the current author it was shown that, when the self-force problem of classical electrodynamics is properly solved, it becomes a plausible ontology underlying the statistical description of…
We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordstr\"om, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider…
Recently the Wigner - Weyl formalism has been applied to the lattice models of solid state physics and to the lattice regularized quantum field theory. This allows to demonstrate that the electric current of intrinsic Anomalous Quantum Hall…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
We present a theoretical study of the excitations on the edge of a two-dimensional electron system in a perpendicular magnetic field in terms of a contour dynamics formalism. In particular, we focus on edge excitations in the quantum Hall…
In this paper, I introduce two new concepts (Minkowski quasi-photon and invariance of physical definitions) to elucidate the theory developed in my previous work [Can. J. Phys. 93, 1510 (2015)], and to clarify the criticisms by Partanen and…
We present a new concept of nonlinear dynamics of incoherent superstrong radiation in plasmas. Recently we have disclosed a novel mechanism of the establishment of equilibrium between a photon and a dense photon bunch through the exchange…
Modification of the right-hand-side of canonical commutation relations (CCR) naturally occurs if one considers a harmonic oscillator with indefinite frequency. Quantization of electromagnetic field by means of such a non-CCR algebra…