Dynamical realizations of l-conformal Newton-Hooke group
arXiv:1303.3419 · doi:10.1016/j.physletb.2013.04.054
Abstract
The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A configuration space of the model involves coordinates, which parametrize a particle moving in d spatial dimensions and a conformal mode, which gives rise to an effective external field.The dynamical system describes a generalized multi-dimensional oscillator, which undergoes accelerated/decelerated motion in an ellipse in accord with evolution of the conformal mode. Higher derivative formulations are discussed as well. It is demonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the l=3/2-conformal Newton-Hooke symmetry for a particular choice of its frequencies.
12 pages
References in corpus (9)
- Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry
- Remarks on l-conformal extension of the Newton-Hooke algebra
- Dynamical realization of l-conformal Galilei algebra and oscillators
- Nonrelativistic conformal groups and their dynamical realizations
- Remark on quantum mechanics with N=2 Schrodinger supersymmetry
- N=2 superconformal Newton-Hooke algebra and many-body mechanics
- N=2 supersymmetric extension of l-conformal Galilei algebra
- New potentials for conformal mechanics
- Acceleration-extended Newton-Hooke symmetry and its dynamical realization
Cited by in corpus (37)
- Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
- Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
- Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
- An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
- On dynamical realizations of l-conformal Galilei groups
- On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
- Ricci-flat spacetimes with l-conformal Galilei symmetry
- Four types of (super)conformal mechanics: D-module reps and invariant actions
- Dynamical realizations of N=1 l-conformal Galilei superalgebra
- Schrödinger symmetry: a historical review
- The odd-order Pais-Uhlenbeck oscillator
- Geometry of the isotropic oscillator driven by the conformal mode
- -oscillators from second-order invariant PDEs of the centrally extended Conformal Galilei Algebras
- Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
- Equations of fluid dynamics with the l-conformal Galilei symmetry
- Minimal realization of -conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation
- Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
- Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
- Remark on higher-derivative mechanics with l-conformal Galilei symmetry
- Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
- New realizations of N=2 l-conformal Newton-Hooke superalgebra
- N=2 supersymmetric Pais-Uhlenbeck oscillator
- On Casimir Operators of Conformal Galilei Algebras
- Higher-derivative generalization of conformal mechanics
- Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
- Invariant PDEs of Conformal Galilei Algebra as deformations: cryptohermiticity and contractions
- Nonlocal dynamics and infinite non-relativistic conformal symmetries
- Perfect fluid dynamics with conformal Newton-Hooke symmetries
- Superfield approach to higher derivative N=1 superconformal mechanics
- On the Schwarzian counterparts of conformal mechanics
- Hidden symmetries of deformed oscillators
- (1+1) Newton-Hooke Group for the Simple and Damped Harmonic Oscillator
- Conformal symmetry in damped Pais-Uhlenbeck oscillator
- SU(1,2) invariance in two-dimensional oscillator
- Nonlinear realizations and the orbit method
- N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
- Circularly polarized periodic gravitational wave and the Pais-Uhlenbeck oscillator