Related papers: Superintegrable relativistic systems in spacetime-…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
We study properties of classical reparametrization-invariant matter systems, mainly the relativistic particle and its d-brane generalization. The corresponding matter Lagrangian naturally contains background interaction fields, such as a…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
The eigenspinor approach uses the classical amplitude of the algebraic Lorentz rotation connecting the lab and rest frames to study the relativistic motion of particles. It suggests a simple covariant extension of the common definition of…
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
We consider superintegrability in classical mechanics in the presence of magnetic fields. We focus on three-dimensional systems which are separable in Cartesian coordinates. We construct all possible minimally and maximally superintegrable…
Schroedinger equations with position dependent mass which are scale invariant and admit second order integrals of motion are classified.
A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory…
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic…
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…
In the paper we investigate the evolution of the relativistic particle (massive and massless) with spin defined by Hamiltonian containing the terms with momentum-spin-orbit coupling. We integrate the corresponding Hamiltonian equations in…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
Electromagnetic field of a fast electric charge in nuclear matter with spatially uniform but random topological charge density is derived. A useful approximation is developed for the relativistic heavy-ion collisions.
A supersymmetric relativistic quantum theory in the temporal domain is developed for bi-spinor fields satisfying the Dirac equation. The simplest time-domain supersymmetric theory can be postulated for fields with time-dependent mass,…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…