Galilean Conformal Mechanics from Nonlinear Realizations

Abstract

We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a non-relativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension D=d+1 (no central charges), as well as in the special dimension D=2+1 with one "exotic" central charge. We obtain new classical mechanics models which extend the standard (D=0+1) conformal mechanics in the presence of d non-vanishing space dimensions.

v2: 1 + 20 pages, small changes in Sect.5 and two references added; the version will appear in Phys.Rev.D

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Cited by in corpus (42)

• Remarks on l-conformal extension of the Newton-Hooke algebra
• Conformal Newton-Hooke symmetry of Pais-Uhlenbeck oscillator
• Dynamical realization of l-conformal Galilei algebra and oscillators
• Dynamical realizations of l-conformal Newton-Hooke group
• Nonrelativistic conformal groups and their dynamical realizations
• Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
• Gauge Fields, Nonlinear Realizations, Supersymmetry
• Effective field theory for spacetime symmetry breaking
• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• On dynamical realizations of l-conformal Galilei groups
• On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
• Intertwining operators for l-conformal Galilei algebras and hierarchy of invariant equations
• Ricci-flat spacetimes with l-conformal Galilei symmetry
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• N=2 supersymmetric extension of l-conformal Galilei algebra
• The algebraic structure of Galilean superconformal symmetries
• Schrödinger symmetry: a historical review
• N=2 supersymmetric particle near extreme Kerr throat
• Geometry of the isotropic oscillator driven by the conformal mode
• Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry
• Equations of fluid dynamics with the l-conformal Galilei symmetry
• A variant of Schwarzian mechanics
• 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
• Conformal mechanics
• Hamiltonian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Quantizations of D=3 Lorentz symmetry
• Dynamical realizations of the Lifshitz group
• Nonlinear realizations, the orbit method and Kohn's theorem
• Lie Symmetries of Non-Relativistic and Relativistic Motions
• Remarks on higher Schwarzians
• Lagrangian formulation for perfect fluid equations with the l-conformal Galilei symmetry
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• Superfield approach to higher derivative N=1 superconformal mechanics
• Galilean Conformal and Superconformal Symmetries
• Treating Ostrogradski instability for Gallilean invariant Chern Simon's model via \mathcal{PT} symmetry
• Casimir operators of centrally extended l-conformal Galilei algebra
• Nonlinear realizations and the orbit method
• Perfect fluid coupled to a solenoidal field which enjoys the l-conformal Galilei symmetry
• New dynamical realizations of the Lifshitz group
• A non-lorentzian primer