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

TL;DR

This paper constructs minimal realizations of the $ ext{ell}$-conformal Galilei algebra and its deformations, linking them to Pais-Uhlenbeck oscillators and gravitational metrics, advancing understanding of symmetry structures in physics.

Contribution

It introduces a minimal realization of the $ ext{ell}$-conformal Galilei group in 2+1 dimensions and constructs invariant actions for its deformation, connecting algebraic structures to physical models.

Findings

Derived complex Pais-Uhlenbeck oscillator equations from minimal realizations.

Constructed invariant actions for deformed $ ext{ell}$=1/2 conformal Galilei algebra.

Found a massive extension of near-horizon Kerr-dS/AdS metric based on new conformal group realization.

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. Schr\"odinger) 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.