Minimal realization of $\ell$-conformal Galilei algebra, Pais-Uhlenbeck oscillators and their deformation

Abstract

We present the minimal realization of the $\ell$-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex Pais-Uhlenbeck oscillator equations. We introduce a minimal deformation of the $\ell$=1/2 conformal Galilei (a.k.a. Schrödinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d=1 conformal group, we find a massive extension of the near-horizon Kerr-dS/AdS metric.

1+12 pages, v2: misprints corrected, 5 refs. added, including on the odd series of PU oscillators, published version

References in corpus (5)

• Remarks on l-conformal extension of the Newton-Hooke algebra
• Hamiltonian formalisms and symmetries of the Pais-Uhlenbeck oscillator
• Dynamical realizations of N=1 l-conformal Galilei superalgebra
• Coset spaces and Einstein manifolds with l-conformal Galilei symmetry
• Remark on higher-derivative mechanics with l-conformal Galilei symmetry

Cited by in corpus (6)

• Schrödinger symmetry: a historical review
• Meta-Schrödinger invariance
• Boundedness of meta-conformal two-point functions in one and two spatial dimensions
• Superfield approach to higher derivative N=1 superconformal mechanics
• Aspects of infinite dimensional $\ell$-super Galilean conformal algebra
• Remarks on Galilean electromagnetism