Armen Nersessian - Academia.edu (original) (raw)
Papers by Armen Nersessian
Physics Letters B, Jun 1, 2005
We construct N = 4 supersymmetric mechanics using the N = 4 nonlinear chiral supermultiplet. The ... more We construct N = 4 supersymmetric mechanics using the N = 4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system.
Physical review, Mar 26, 2003
We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various prope... more We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on I CP N qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the "axially symmetric" system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on I CP 2 and construct some generalized MIC-Kepler problem. We also define a N = 2 superextension of the oscillator on I CP N and show that for N > 1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.
SSRN Electronic Journal
Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a fe... more Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a few interesting observations on its properties [1]. In this paper we use the formulation of the Euler top as a system on complex projective plane, playing the role of phase space, i.e. as a onedimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yieldsá priori integrable family of N = 2k supersymmetric Hamiltonians parameterized by N /2 arbitrary real functions.
Proceedings of the YSU A: Physical and Mathematical Sciences, 2016
We describe the integrals of motion of the high-dimensional Coulomb system with and without the S... more We describe the integrals of motion of the high-dimensional Coulomb system with and without the Stark term, perturbed by the Calogero interaction.
Теоретическая и математическая физика, 1998
Physical review, Jun 7, 2016
We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the... more We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and its restriction to (Coxeter reflection) symmetric wave functions. By the same method we also find the symmetry generators and compute their algebras.
![Research paper thumbnail of Erratum: (Super) oscillator on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>CP</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>and a constant magnetic field [Phys. Rev. D<b>67</b>, 065013 (2003)]](https://attachments.academia-assets.com/110296415/thumbnails/1.jpg)
](Physical review, Apr 8, 2005
We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various prope... more We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on I CP N qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the "axially symmetric" system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on I CP 2 and construct some generalized MIC-Kepler problem. We also define a N = 2 superextension of the oscillator on I CP N and show that for N > 1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.
Physical review, Jun 7, 2001
The geometric models of N = 4 supersymmetric mechanics with (2d.2d) I C-dimensional phase space a... more The geometric models of N = 4 supersymmetric mechanics with (2d.2d) I C-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N = 2 supersymmetric sigma-models by Alvarez-Gaumé and Freedman. The related construction of supersymmetric mechanics whose phase space is a Kähler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.
arXiv (Cornell University), Oct 2, 2022
We consider the propagation of polarized light in the medium with isotropic refraction index prof... more We consider the propagation of polarized light in the medium with isotropic refraction index profile and show that polarization violates the additional symmetries of the medium. Then we suggest a scheme for the construction of polarization-dependent refraction index which restores all symmetries of the initial profile. We illustrate the proposed scheme on the examples of Luneburg and Maxwell's fisheye profiles.
arXiv (Cornell University), Oct 22, 2021
We suggest the su(1, N |M)-superconformal mechanics formulated in terms of phase superspace given... more We suggest the su(1, N |M)-superconformal mechanics formulated in terms of phase superspace given by the non-compact analogue of complex projective superspace.We parameterized this phase space by the specific coordinates allowing to interpret it as a higher-dimensional super-analogue of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we introduced the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we demonstrated that proposed scheme allows to construct the su(1, N |M) supeconformal extensions of wide class of superintegrable systems. We also proposed the superintegrable oscillator-and Coulomb-like systems with a su(1, N |M) dynamical superalgebra, and found that oscillator-like systems admit deformed N = 2M Poincaré supersymmetry, in contrast with Coulomb-like ones.
arXiv (Cornell University), Nov 9, 2017
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curve... more We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in application to (typically, superintegrable) problems whose energy spectrum is given by a quadratic function of the energy level number, since for such systems the spacetimes one obtains possess evenly spaced, resonant spectra of frequencies for scalar fields of a certain mass. This construction emerges as a generalization of the previously studied correspondence between the Higgs oscillator and Anti-de Sitter spacetime, which has been useful for both understanding weakly nonlinear dynamics in Anti-de Sitter spacetime and algebras of conserved quantities of the Higgs oscillator. Our conversion procedure ("Klein-Gordonization") reduces to a nonlinear elliptic equation closely reminiscent of the one emerging in relation to the celebrated Yamabe problem of differential geometry. As an illustration, we explicitly demonstrate how to apply this procedure to superintegrable Rosochatius systems, resulting in a large family of spacetimes with resonant spectra for massless wave equations.
arXiv (Cornell University), Oct 2, 2017
We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from R n to... more We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from R n to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with N = 4 supersymmetric n-dimensional mechanics from flat to curved space. The resulting 'curved WDVV equation' is written in terms of a third-rank Codazzi tensor. For every flat-space WDVV solution subject to a simple constraint we provide a curved-space solution on any isotropic space, in terms of the rotationally invariant conformal factor of the metric.
arXiv (Cornell University), Nov 14, 2002
A bstract W e propose an extended B R ST i nvari ant Lagrangi an quanti zati on schem e of genera... more A bstract W e propose an extended B R ST i nvari ant Lagrangi an quanti zati on schem e of generalgauge theori es based on expl i ci t real i zati on of"m odi ed tri pl ecti c al gebra" i n generalcoordi nates. A l lthe know n Lagrangi an quanti zati on schem es based on the extended B R ST sym m etry are obtai ned by speci fyi ng the (free) param eters of that m ethod.
Physics Letters B, 2005
We propose the Hamiltonian model of N = 8 supersymmetric mechanics on n−dimensional special Kähle... more We propose the Hamiltonian model of N = 8 supersymmetric mechanics on n−dimensional special Kähler manifolds (of the rigid type).
Physics of Particles and Nuclei, Sep 1, 2018
Physics of Particles and Nuclei Letters, Mar 1, 2017
We present N=4 supersymmetric mechanics on n-dimensional Riemannian manifolds constructed within ... more We present N=4 supersymmetric mechanics on n-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten–Dijkgraaf–Verlinde–Verlinde equations specified by the presence of the manifold’s curvature tensor. Solutions of original Witten–Dijkgraaf–Verlinde–Verlinde equations and related prepotentials defining N=4 superconformal mechanics in flat space can be lifted to so(n)-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of n copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.
Physics of Atomic Nuclei, 2017
We show that the Calogero-type perturbation preserves the integrability and partial separation of... more We show that the Calogero-type perturbation preserves the integrability and partial separation of variables for the Stark-Coulomb and two-center Coulomb problems, and present the explicit expressions of their constants of motion. We reveal that this perturbation preserves the spectra of initial systems, but leads to the change of degree of degeneracy.
Physics Letters B, Jun 1, 2005
We construct N = 4 supersymmetric mechanics using the N = 4 nonlinear chiral supermultiplet. The ... more We construct N = 4 supersymmetric mechanics using the N = 4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system.
Physical review, Mar 26, 2003
We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various prope... more We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on I CP N qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the "axially symmetric" system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on I CP 2 and construct some generalized MIC-Kepler problem. We also define a N = 2 superextension of the oscillator on I CP N and show that for N > 1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.
SSRN Electronic Journal
Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a fe... more Recently A.Galajinsky has suggested the N = 1 supersymmetric extension of Euler top and made a few interesting observations on its properties [1]. In this paper we use the formulation of the Euler top as a system on complex projective plane, playing the role of phase space, i.e. as a onedimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yieldsá priori integrable family of N = 2k supersymmetric Hamiltonians parameterized by N /2 arbitrary real functions.
Proceedings of the YSU A: Physical and Mathematical Sciences, 2016
We describe the integrals of motion of the high-dimensional Coulomb system with and without the S... more We describe the integrals of motion of the high-dimensional Coulomb system with and without the Stark term, perturbed by the Calogero interaction.
Теоретическая и математическая физика, 1998
Physical review, Jun 7, 2016
We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the... more We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and its restriction to (Coxeter reflection) symmetric wave functions. By the same method we also find the symmetry generators and compute their algebras.
Physical review, Apr 8, 2005
We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various prope... more We define the "maximally integrable" isotropic oscillator on I CP N and discuss its various properties, in particular, the behaviour of the system with respect to a constant magnetic field. We show that the properties of the oscillator on I CP N qualitatively differ in the N > 1 and N = 1 cases. In the former case we construct the "axially symmetric" system which is locally equivalent to the oscillator. We perform the Kustaanheimo-Stiefel transformation of the oscillator on I CP 2 and construct some generalized MIC-Kepler problem. We also define a N = 2 superextension of the oscillator on I CP N and show that for N > 1 the inclusion of a constant magnetic field preserves the supersymmetry of the system.
Physical review, Jun 7, 2001
The geometric models of N = 4 supersymmetric mechanics with (2d.2d) I C-dimensional phase space a... more The geometric models of N = 4 supersymmetric mechanics with (2d.2d) I C-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N = 2 supersymmetric sigma-models by Alvarez-Gaumé and Freedman. The related construction of supersymmetric mechanics whose phase space is a Kähler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.
arXiv (Cornell University), Oct 2, 2022
We consider the propagation of polarized light in the medium with isotropic refraction index prof... more We consider the propagation of polarized light in the medium with isotropic refraction index profile and show that polarization violates the additional symmetries of the medium. Then we suggest a scheme for the construction of polarization-dependent refraction index which restores all symmetries of the initial profile. We illustrate the proposed scheme on the examples of Luneburg and Maxwell's fisheye profiles.
arXiv (Cornell University), Oct 22, 2021
We suggest the su(1, N |M)-superconformal mechanics formulated in terms of phase superspace given... more We suggest the su(1, N |M)-superconformal mechanics formulated in terms of phase superspace given by the non-compact analogue of complex projective superspace.We parameterized this phase space by the specific coordinates allowing to interpret it as a higher-dimensional super-analogue of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we introduced the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we demonstrated that proposed scheme allows to construct the su(1, N |M) supeconformal extensions of wide class of superintegrable systems. We also proposed the superintegrable oscillator-and Coulomb-like systems with a su(1, N |M) dynamical superalgebra, and found that oscillator-like systems admit deformed N = 2M Poincaré supersymmetry, in contrast with Coulomb-like ones.
arXiv (Cornell University), Nov 9, 2017
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curve... more We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in application to (typically, superintegrable) problems whose energy spectrum is given by a quadratic function of the energy level number, since for such systems the spacetimes one obtains possess evenly spaced, resonant spectra of frequencies for scalar fields of a certain mass. This construction emerges as a generalization of the previously studied correspondence between the Higgs oscillator and Anti-de Sitter spacetime, which has been useful for both understanding weakly nonlinear dynamics in Anti-de Sitter spacetime and algebras of conserved quantities of the Higgs oscillator. Our conversion procedure ("Klein-Gordonization") reduces to a nonlinear elliptic equation closely reminiscent of the one emerging in relation to the celebrated Yamabe problem of differential geometry. As an illustration, we explicitly demonstrate how to apply this procedure to superintegrable Rosochatius systems, resulting in a large family of spacetimes with resonant spectra for massless wave equations.
arXiv (Cornell University), Oct 2, 2017
We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from R n to... more We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from R n to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with N = 4 supersymmetric n-dimensional mechanics from flat to curved space. The resulting 'curved WDVV equation' is written in terms of a third-rank Codazzi tensor. For every flat-space WDVV solution subject to a simple constraint we provide a curved-space solution on any isotropic space, in terms of the rotationally invariant conformal factor of the metric.
arXiv (Cornell University), Nov 14, 2002
A bstract W e propose an extended B R ST i nvari ant Lagrangi an quanti zati on schem e of genera... more A bstract W e propose an extended B R ST i nvari ant Lagrangi an quanti zati on schem e of generalgauge theori es based on expl i ci t real i zati on of"m odi ed tri pl ecti c al gebra" i n generalcoordi nates. A l lthe know n Lagrangi an quanti zati on schem es based on the extended B R ST sym m etry are obtai ned by speci fyi ng the (free) param eters of that m ethod.
Physics Letters B, 2005
We propose the Hamiltonian model of N = 8 supersymmetric mechanics on n−dimensional special Kähle... more We propose the Hamiltonian model of N = 8 supersymmetric mechanics on n−dimensional special Kähler manifolds (of the rigid type).
Physics of Particles and Nuclei, Sep 1, 2018
Physics of Particles and Nuclei Letters, Mar 1, 2017
We present N=4 supersymmetric mechanics on n-dimensional Riemannian manifolds constructed within ... more We present N=4 supersymmetric mechanics on n-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant constancy equations as well as modified Witten–Dijkgraaf–Verlinde–Verlinde equations specified by the presence of the manifold’s curvature tensor. Solutions of original Witten–Dijkgraaf–Verlinde–Verlinde equations and related prepotentials defining N=4 superconformal mechanics in flat space can be lifted to so(n)-invariant Riemannian manifolds. For the Hamiltonian this lift generates an additional potential term which, on spheres and (two-sheeted) hyperboloids, becomes a Higgs-oscillator potential. In particular, the sum of n copies of one-dimensional conformal mechanics results in a specific superintegrable deformation of the Higgs oscillator.
Physics of Atomic Nuclei, 2017
We show that the Calogero-type perturbation preserves the integrability and partial separation of... more We show that the Calogero-type perturbation preserves the integrability and partial separation of variables for the Stark-Coulomb and two-center Coulomb problems, and present the explicit expressions of their constants of motion. We reveal that this perturbation preserves the spectra of initial systems, but leads to the change of degree of degeneracy.