Related papers: Motion in a symmetric potential on the hyperbolic …
There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant negative curvature, hyperbolic plane, in presence of an external magnetic field, analogue of the…
The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…
We present quantization of particle dynamics on one-sheet hyperboloid embedded in three dimensional Minkowski space. Taking account of all global symmetries enables unique quantization. Making use of topology of canonical variables not only…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
We propose the model of massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle follow from the fact that all the classical paths of the particle lie on a cylinder whose position in…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
We analyze particle dynamics on $N$ dimensional one-sheet hyperboloid embedded in $N+1$ dimensional Minkowski space. The dynamical integrals constructed by $SO_\uparrow (1,N)$ symmetry of spacetime are used for the gauge-invariant…
We construct the hyperbolic plane with its geodesic flow as the scale plus symmetry reduction of a three-body problem in the Euclidean plane. The potential is $-I/\Delta^2$ where $I$ is the triangle's moment of inertia and $\Delta$ its…
We consider the quantum dynamics of a single particle in the plane under the influence of a constant perpendicular magnetic and a crossed electric potential field. For a class of smooth and small potentials we construct a non-trivial…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
The motion of a particle that suffers the influence of simple inner (outer) periodic perturbations when it evolves around a center of attraction modeled by an inverse square law plus a quadrupole-like term is studied. The equations of…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…
Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with…
We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up…
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…
This paper we consider for the N-body problem with potential 1/r{\alpha} (0 < {\alpha} < 1) the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. Here E is the Euclidean space…
We consider motion in a periodic potential in a classical, quantum, and semiclassical context. Various results on the distribution of asymptotic velocities are proven.
We consider the motion of a particle along the geodesic lines of the Poincar\`e half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version…
Using a hyperbolic complex plane, we study the realization of the underlying hyperbolic symmetry as an internal symmetry that enables the unification of scalar fields of cosmological and particle physics interest. Such an unification is…