Quantization on the Cone and Cyon-Oscillator Duality

TL;DR

This paper demonstrates a duality between a three-dimensional isotropic oscillator constrained to a cone and a planar particle-vortex system exhibiting fractional statistics, revealing a novel connection in quantum systems.

Contribution

It introduces a new duality linking the cone-restricted oscillator to the particle-vortex system, expanding understanding of quantum dualities.

Findings

Establishes the duality between the cone oscillator and the cyon system.

Provides a mathematical framework for the duality.

Highlights implications for fractional statistics and quantum systems.

Abstract

It is shown that the three-dimensional isotropic oscillator with coordinates belonging to the two-dimensional half-up cone is dual to the cyon , i.e. the planar particle-vortex bound system provided by fractional statistics.