Related papers: Generalizations of MICZ-Kepler system
We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic…
By using Meng's idea in his generalization of the classical MICZ-Kepler problem, we obtained the equations of motion of a charged particle in the field of generalized Dirac monopole in odd dimensional Euclidean spaces. The main result is…
We show that the n-dimensional MICZ-Kepler system arises from symplectic reduction of a simple mechanical system on the cone over the rotation group SO(n). As a corollary we derive an elementary formula for its general solution. The…
This paper deals with dynamical system that generalizes the MIC-Kepler system. It is shown that the Schr\"{o}dinger equation for this generalized MIC-Kepler system can be separated in spherical and parabolic coordinates. The spectral…
The quantum two-center MICZ--Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits…
We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and (two-sheet) hyperboloid. We then construct their energy spectra and normalized wave functions, concluding that the suggested systems are minimally…
We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space $E_{3}$ and its dual the four dimensional singular oscillator in four-dimensional Euclidean space $E_{4}$. We present their…
We present a generalization of the coupled dipole method to the scattering of light by arbitrary periodic structures. This new formulation of the coupled dipole method relies on the same direct-space discretization scheme that is widely…
We quantize a generalized electromagnetism in 2 + 1 dimensions which contains a higher-order derivative term by using Dirac's method. By introducing auxiliary fields we transform the original theory in a lower-order derivative one which can…
We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical…
We consider various generalizations of the Kepler problem to three-dimensional sphere $S^3$, a compact space of constant curvature. These generalizations include, among other things, addition of a spherical analog of the magnetic monopole…
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
In the present paper, dynamics of generalized charged particles are studied in the presence of external electromagnetic interactions. This particular extension of the free relativistic particle model lives in Non-Commutative…
The Kepler problem is a physical problem about two bodies which attract each other by a force proportional to the inverse square of the distance. The MICZ-Kepler problems are its natural cousins and have been previously generalized from…
Segal's hypothesis that physical theories drift toward simple groups follows from a general quantum principle and suggests a general quantization process. I general-quantize the scalar meson field in Minkowski space-time to illustrate the…
The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with…
There have been several attempts in recent years to extend the notions of symplectic and Poisson structures in order to create a suitable geometrical framework for classical field theories, trying to achieve a success similar to the use of…
It is shown that the generalized MIC-Kepler system and four-dimensional singular oscillator are dual to each other and the duality transformation is the generalized version of the Kustaanheimo-Stiefel transformation.
A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-H\"uckel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions…
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…