Nonrelativistic conformal groups and their dynamical realizations

Abstract

Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables. It is shown that the corresponding dynamical system describes, within Ostrogradski framework, the nonrelativistic particle obeying (N+1)-th order equation of motion. As a special case, the Schroedinger group and the standard Newton equations are obtained for N=1 (l=1/2).

18 pages, no figures; few references added

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Cited by in corpus (34)

• Dynamical realization of l-conformal Galilei algebra and oscillators
• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Dynamical realizations of l-conformal Newton-Hooke group
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• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• On dynamical realizations of l-conformal Galilei groups
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Newton-Hooke type symmetry of anisotropic oscillators
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• N=2 supersymmetric extension of l-conformal Galilei algebra
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Chiral and Real N=2 supersymmetric l-conformal Galilei algebras
• N = 2 Galilean superconformal algebras with central extension
• The odd-order Pais-Uhlenbeck oscillator
• Nonrelativistic conformal transformations in Lagrangian formalism
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Unitary representations of N-conformal Galilei group
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry
• Group theoretical construction of planar Noncommutative Phase Spaces
• A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras
• More on the operator-state map in non-relativistic CFTs
• Invariant PDEs with Two-dimensional Exotic Centrally Extended Conformal Galilei Symmetry
• New realizations of N=2 l-conformal Newton-Hooke superalgebra
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• On Casimir Operators of Conformal Galilei Algebras
• Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
• Superfield approach to higher derivative N=1 superconformal mechanics
• Casimir operators of centrally extended l-conformal Galilei algebra
• Nonlinear realizations and the orbit method
• The Lie algebra of the lowest transitively differential group of degree three
• 2-local derivation on the conformal Galilei algebra