(2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase

Abstract

A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed.

30 pages, 2 figures; typos corrected

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Cited by in corpus (72)

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• Coset Construction for Duals of Non-relativistic CFTs
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• Galilean Conformal Mechanics from Nonlinear Realizations
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
• Noncommutative oscillator, symmetry and Landau problem
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• Potentials in N=4 superconformal mechanics
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• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
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• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
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• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
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• The odd-order Pais-Uhlenbeck oscillator
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-relativistic limits and three-dimensional coadjoint Poincare gravity
• Three-dimensional non-relativistic supergravity and torsion
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• Enlarged NH symmetries: Particle Dynamics and Gauge Symmetries
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• Gravitational Waves and Conformal Time Transformations
• Acceleration-extended Newton-Hooke symmetry and its dynamical realization
• Quantum Degenerate Systems
• Extended Kinematical 3D Gravity Theories
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
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• On Casimir Operators of Conformal Galilei Algebras
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• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• Nonlinear realizations, the orbit method and Kohn's theorem
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• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Beyond the Relativistic Point Particle: A Reciprocally Invariant System and its Generalisation
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Conformal bridge in a cosmic string background
• Symmetries of the Free Schrödinger Equation in the Non-Commutative Plane
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• Exotic Non-relativistic String
• Galilean Conformal and Superconformal Symmetries
• Removal of instabilities of the higher derivative theories in the light of antilinearity
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• Higher-derivative superparticle in AdS${}_3$ space
• Three-dimensional non-relativistic Hietarinta supergravity
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
• Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension
• A general action for a particle in 2+1 anti-de Sitter space