A. Nersessian - Academia.edu (original) (raw)

Papers by A. Nersessian

arXiv: High Energy Physics - Theory, 2002

We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of "modified triplectic algebra" in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

We review the classical properties of Tremblay–Turbiner–Winternitz and Post–Wintenitz systems and... more We review the classical properties of Tremblay–Turbiner–Winternitz and Post–Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in s proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action–angle variables. DOI: 10.1134/S1063778817030085

We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of ”modified triplectic algebra” in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

Journal of Physics: Conference Series

We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersym... more We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.

Physics of Atomic Nuclei

We study geodesics on the near horizon geometry of odd-dimensional Myers–Perry black hole in the ... more We study geodesics on the near horizon geometry of odd-dimensional Myers–Perry black hole in the extremal vanishing horizon (EVH) limit. Knowing the fact that geodesics equations on Myers–Perry black hole are integrable in ellipsoidal coordinates, we take the near horizon limit in this coordinate system and obtain the near horizon EVH geometry and its Killing tensors. We explicitly show that geodesics equations are integrable on the near horizon EVH geometry ofMyers–Perry and compute the constants of motion. The resultant Killing tensors of this constants of motion matches with the Killing tensors given by taking the near-horizon limit.

Physics Letters A, 2014

We reexamine the model of relativistic particle with higher-derivative term linear on the first e... more We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation.

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We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of "modified triplectic algebra" in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massi... more The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space time are studied. It is shown that the modified system remains spinless and possesses extended gauge invariance. Though the torsion term does not generate spin, it provides the system with a nontrivial mass spectrum, described by onedimensional conformal mechanics. Under an appropriate choice of characteristic constants the system has solutions with a discrete mass spectrum.

We give a simple geometric explanation for the similarity transformation mapping one-dimensional ... more We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) f I CP 1. We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobachevsky superspace f I CP 1|k .

The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. ... more The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" ("charge-Z 2-dyon) with a half-spin, is constructed by reducing the quantum circular oscillator with respect to the action of the parity operator. The other two systems are constructed by reduction from the two-dimensional complex space. The first system is a particle on the sphere in the presence of the exterior constant magnetic field (generated by Dirac's monopole located in its center). This system is dual to the massless (3+1)-dimensional particle with fixed energy. The second system represents the particle on the pseudosphere in the presence of exterior magnetic field and is dual to the massive relativistic anyon.

We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric qua... more We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric quantization formalism-triplectic quantization-recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry.

We demonstrate that two-dimensional N = 8 supersymmetric quantum mechanics which inherits the mos... more We demonstrate that two-dimensional N = 8 supersymmetric quantum mechanics which inherits the most interesting properties of N = 2, d = 4 SYM can be constructed if the reduction to one dimension is performed in terms of the basic object, i.e. the N = 2, d = 4 vector multiplet. In such a reduction only complex scalar fields from the N = 2, d = 4 vector multiplet become physical bosons in d = 1, while the rest of the bosonic components are reduced to auxiliary fields, thus giving rise to the (2, 8, 6) supermultiplet in d = 1. We construct the most general action for this supermultiplet with all possible Fayet-Iliopoulos terms included and explicitly demonstrate that the action possesses duality symmetry extended to the fermionic sector of theory. In order to deal with the second-class constraints present in the system, we introduce the Dirac brackets for the canonical variables and find the supercharges and Hamiltonian which form a N = 8 super Poincarè algebra with central charges. Finally, we explicitly present the generalization of two-dimensional N = 8 supersymmetric quantum mechanics to the 2kdimensional case with a special Kähler geometry in the target space.

We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (wit... more We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Keplerlike one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

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).

Arxiv preprint hep-th/9812077, 1998

The search for lagrangians describing spinning par-ticles, both massive and massless, has a long ... more The search for lagrangians describing spinning par-ticles, both massive and massless, has a long history. The conventional approach is based on an extension of Minkowski space-time by auxiliary grassmann variables which, after quantization, provide the extra degrees of ...

The transparent way for the invariant (Hamiltonian) description of equivariant localization of th... more The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits straightforward generalization for the path integrals. Simultaneously the method of supersymmetrization for a wide class of the Hamiltonian systems is derived.

We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of ... more We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are de ned by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.

We suggested a geometric approach to address the external field influence on the DNA molecules, d... more We suggested a geometric approach to address the external field influence on the DNA molecules, described by the WLC model via geometric coupling. It consists in the introduction of the effective metrics depending on the potential of the external field, with further re-definition of the arc-length parameter and of the extrinsic curvatures of the DNA molecules. It yields the nontrivial impact of the external field in the internal energy of macromolecules. We give the Hamiltonian formulation of this model and perform its preliminary analysis in the redefinition of the initial energy density.

arXiv: High Energy Physics - Theory, 2002

We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of "modified triplectic algebra" in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

We review the classical properties of Tremblay–Turbiner–Winternitz and Post–Wintenitz systems and... more We review the classical properties of Tremblay–Turbiner–Winternitz and Post–Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in s proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action–angle variables. DOI: 10.1134/S1063778817030085

We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of ”modified triplectic algebra” in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

Journal of Physics: Conference Series

We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersym... more We extend the relation between the Witten-Dijkgraaf-Verlinde-Verlinde equation and N = 4 supersymmetric mechanics to arbitrary curved spaces. The resulting curved WDVV equation is written in terms of the third rank Codazzi tensor. We provide the solutions of the curved WDVV equation for the so(n) symmetric conformally flat metrics. We also explicitly demonstrate how each solution of the flat WDVV equation can be lifted up to the curved WDVV solution on the conformally flat spaces.

Physics of Atomic Nuclei

We study geodesics on the near horizon geometry of odd-dimensional Myers–Perry black hole in the ... more We study geodesics on the near horizon geometry of odd-dimensional Myers–Perry black hole in the extremal vanishing horizon (EVH) limit. Knowing the fact that geodesics equations on Myers–Perry black hole are integrable in ellipsoidal coordinates, we take the near horizon limit in this coordinate system and obtain the near horizon EVH geometry and its Killing tensors. We explicitly show that geodesics equations are integrable on the near horizon EVH geometry ofMyers–Perry and compute the constants of motion. The resultant Killing tensors of this constants of motion matches with the Killing tensors given by taking the near-horizon limit.

Physics Letters A, 2014

We reexamine the model of relativistic particle with higher-derivative term linear on the first e... more We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation.

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We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories ba... more We propose an extended BRST invariant Lagrangian quantization scheme of general gauge theories based on explicit realization of "modified triplectic algebra" in general coordinates. All the known Lagrangian quantization schemes based on the extended BRST symmetry are obtained by specifying the (free) parameters of that method.

The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massi... more The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space time are studied. It is shown that the modified system remains spinless and possesses extended gauge invariance. Though the torsion term does not generate spin, it provides the system with a nontrivial mass spectrum, described by onedimensional conformal mechanics. Under an appropriate choice of characteristic constants the system has solutions with a discrete mass spectrum.

We give a simple geometric explanation for the similarity transformation mapping one-dimensional ... more We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) f I CP 1. We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobachevsky superspace f I CP 1|k .

The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. ... more The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" ("charge-Z 2-dyon) with a half-spin, is constructed by reducing the quantum circular oscillator with respect to the action of the parity operator. The other two systems are constructed by reduction from the two-dimensional complex space. The first system is a particle on the sphere in the presence of the exterior constant magnetic field (generated by Dirac's monopole located in its center). This system is dual to the massless (3+1)-dimensional particle with fixed energy. The second system represents the particle on the pseudosphere in the presence of exterior magnetic field and is dual to the massive relativistic anyon.

We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric qua... more We give a simple geometrical picture of the basic structures of the covariant Sp(2) symmetric quantization formalism-triplectic quantization-recently suggested by Batalin, Marnelius and Semikhatov. In particular, we show that the appearance of an even Poisson bracket is not a particular property of triplectic quantization. Rather, any solution of the classical master equation generates on a Lagrangian surface of the antibracket an even Poisson bracket. Also other features of triplectic quantization can be identified with aspects of conventional Lagrangian BRST quantization without extended BRST symmetry.

We demonstrate that two-dimensional N = 8 supersymmetric quantum mechanics which inherits the mos... more We demonstrate that two-dimensional N = 8 supersymmetric quantum mechanics which inherits the most interesting properties of N = 2, d = 4 SYM can be constructed if the reduction to one dimension is performed in terms of the basic object, i.e. the N = 2, d = 4 vector multiplet. In such a reduction only complex scalar fields from the N = 2, d = 4 vector multiplet become physical bosons in d = 1, while the rest of the bosonic components are reduced to auxiliary fields, thus giving rise to the (2, 8, 6) supermultiplet in d = 1. We construct the most general action for this supermultiplet with all possible Fayet-Iliopoulos terms included and explicitly demonstrate that the action possesses duality symmetry extended to the fermionic sector of theory. In order to deal with the second-class constraints present in the system, we introduce the Dirac brackets for the canonical variables and find the supercharges and Hamiltonian which form a N = 8 super Poincarè algebra with central charges. Finally, we explicitly present the generalization of two-dimensional N = 8 supersymmetric quantum mechanics to the 2kdimensional case with a special Kähler geometry in the target space.

We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (wit... more We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Keplerlike one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

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).

Arxiv preprint hep-th/9812077, 1998

The search for lagrangians describing spinning par-ticles, both massive and massless, has a long ... more The search for lagrangians describing spinning par-ticles, both massive and massless, has a long history. The conventional approach is based on an extension of Minkowski space-time by auxiliary grassmann variables which, after quantization, provide the extra degrees of ...

The transparent way for the invariant (Hamiltonian) description of equivariant localization of th... more The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits straightforward generalization for the path integrals. Simultaneously the method of supersymmetrization for a wide class of the Hamiltonian systems is derived.

We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of ... more We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are de ned by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.

We suggested a geometric approach to address the external field influence on the DNA molecules, d... more We suggested a geometric approach to address the external field influence on the DNA molecules, described by the WLC model via geometric coupling. It consists in the introduction of the effective metrics depending on the potential of the external field, with further re-definition of the arc-length parameter and of the extrinsic curvatures of the DNA molecules. It yields the nontrivial impact of the external field in the internal energy of macromolecules. We give the Hamiltonian formulation of this model and perform its preliminary analysis in the redefinition of the initial energy density.