(2+1)D Exotic Newton-Hooke Symmetry, Duality and Projective Phase

TL;DR

This paper constructs a (2+1)D particle model with exotic Newton-Hooke symmetry, revealing three phases, duality relations, and connections to noncommutative geometry, with implications for wave equations and symmetry representations.

Contribution

It introduces a new particle system with exotic Newton-Hooke symmetry, analyzing its phases, dualities, and wave equations, expanding understanding of noncommutative and symmetry structures in lower-dimensional physics.

Findings

Three distinct phases depending on central charges

Duality transformation relates subcritical and supercritical phases

Wave equations with projective symmetry representations

Abstract

A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton-Hooke symmetry are constructed.