Armen Nersessian

Two phases of the noncommutative quantum mechanics

We consider quantum mechanics on the noncommutative plane in the presence of magnetic field B. We show, that the model has two essentially different phases separated by the point Bθ=cℏ2/e, where θ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When κ=1−eBθ/cℏ2 0 the number of states is infinite. The perturbative spectrum near the critical point κ=0 is computed.

Relation of the oscillator and Coulomb systems on spheres and pseudospheres

It is shown, that oscillators on the sphere and the pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere. The even states of an oscillator yield the conventional Coulomb system on the pseudosphere, while the odd states yield the Coulomb system on the pseudosphere in the presence of magnetic flux tube generating spin

Hidden symmetries of integrable conformal mechanical systems

1/2.

MASSIVE SPINNING PARTICLES AND THE GEOMETRY OF NULL CURVES

A similar relation is established for the oscillator on the (pseudo)sphere specified by the presence of constant uniform magnetic field

The cuboctahedric Higgs oscillator from the rational Calogero model

{B}_{0}

Second Hopf map and supersymmetric mechanics with a Yang monopole

and the Coulomb-like system on pseudosphere specified by the presence of the magnetic field

A NOTE ON QUANTUM BOHLIN TRANSFORMATION

{(B/2r}_{0})(|{x}_{3}/\mathbf{x}|\ensuremath{-}\ensuremath{\epsilon}).

Invariants of the spherical sector in conformal mechanics

The correspondence between the oscillator and the Coulomb systems the higher dimensions is also discussed.

Multicenter McIntosh-Cisneros-Zwanziger-Kepler system, supersymmetry and integrability

Abstract We split the generic conformal mechanical system into a “radial” and an “angular” part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N = 4 supersymmetric “angular” Hamiltonian system one may construct a new system with full N = 4 superconformal D ( 1 , 2 ; α ) symmetry.

Integrable generalizations of oscillator and Coulomb systems via action–angle variables

Abstract We study the simplest geometrical particle model associated with null paths in four-dimensional Minkowski space-time. The action is given by the pseudo-arclength of the particle worldline. We show that the reduced classical phase space of this system coincides with that of a massive spinning particle of spin s = α 2 / M , where M is the particle mass, and α is the coupling constant in front of the action. Consistency of the associated quantum theory requires the spin s to be an integer or half integer number, thus implying a quantization condition on the physical mass M of the particle. Then, standard quantization techniques show that the corresponding Hilbert spaces are solution spaces of the standard relativistic massive wave equations. Therefore this geometrical particle model provides us with an unified description of Dirac fermions ( s =1/2) and massive higher spin fields.