Conformal mechanics in Newton-Hooke spacetime

Abstract

Conformal many-body mechanics in Newton-Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N=2 superconformal extension is built and a new class on N=2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N=2 quantum mechanics in Newton-Hooke spacetime is discussed.

V2: references added; the version to appear in NPB

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Cited by in corpus (49)

• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Remarks on l-conformal extension of the Newton-Hooke algebra
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Cosmological aspects of the Eisenhart-Duval lift
• Dynamical realizations of l-conformal Newton-Hooke group
• N=2 superparticle near horizon of extreme Kerr-Newman-AdS-dS black hole
• Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
• On dynamical realizations of l-conformal Galilei groups
• Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
• Newton-Hooke type symmetry of anisotropic oscillators
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• Kohn's theorem and Newton-Hooke symmetry for Hill's equations
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Kohn's theorem and Galilean symmetry
• Chiral decomposition in the non-commutative Landau problem
• New potentials for conformal mechanics
• Klein four-group and Darboux duality in conformal mechanics
• The odd-order Pais-Uhlenbeck oscillator
• Kohn condition and exotic Newton-Hooke symmetry in the non-commutative Landau problem
• Proper time reparametrization in cosmology: Mobius symmetry and Kodama charges
• Geometry of the isotropic oscillator driven by the conformal mode
• Conformal bridge transformation and PT symmetry
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Group theoretical construction of planar Noncommutative Phase Spaces
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Galilean conformal algebras in two spatial dimension
• Free Particle Wave Function and Niederer's Transformation
• N=2 supersymmetric Pais-Uhlenbeck oscillator
• N=4 l-conformal Galilei superalgebra
• New realizations of N=2 l-conformal Newton-Hooke superalgebra
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Higher-derivative generalization of conformal mechanics
• N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets
• Twist Deformations of the Supersymmetric Quantum Mechanics
• Superfield approach to higher derivative N=1 superconformal mechanics
• Conformal bridge in a cosmic string background
• Perfect fluid dynamics with conformal Newton-Hooke symmetries
• Conformal symmetry in damped Pais-Uhlenbeck oscillator
• Nonlinear realizations and the orbit method
• N=1,2,3 l-conformal Galilei superalgebras
• Higher-derivative superparticle in AdS${}_3$ space
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• Oscillators from nonlinear realizations
• Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension
• Hidden symmetries and nonlinear (super)algebras