New realizations of N=2 l-conformal Newton-Hooke superalgebra

TL;DR

This paper constructs new representations of the N=2 l-conformal Newton-Hooke superalgebra using Niederer-like transformations and proposes a variant of the supersymmetric Pais-Uhlenbeck oscillator, highlighting advantages over previous models.

Contribution

It introduces novel realizations of the N=2 l-conformal Newton-Hooke superalgebra and a new variant of the supersymmetric Pais-Uhlenbeck oscillator.

Findings

Constructed superalgebra representations with differential operators.

Proposed a new supersymmetric Pais-Uhlenbeck oscillator variant.

Discussed advantages over previous realizations.

Abstract

By applying Niederer--like transformation, we construct a representation of the N=2 l-conformal Newton-Hooke superalgebra for the case of a negative cosmological constant in terms of linear differential operators as well as its dynamical realization. Another variant of N=2 supersymmetric Pais-Uhlenbeck oscillator for a particular choice of its frequencies is proposed. The advantages of such realizations as compared to their analogues introduced in [J. Math. Phys. 53 (2012) 072904], [J. Math. Phys. 56 (2015) 022902] are discussed.