N=1, D=3 Superanyons, osp(2|2) and the Deformed Heisenberg Algebra

TL;DR

This paper develops a supersymmetric quantum model for fractional spin particles in 2+1 dimensions, revealing hidden symmetries and connecting to deformed harmonic oscillators, advancing understanding of supersymmetric anyons.

Contribution

It introduces a novel N=1 supersymmetric extension of a fractional spin particle model with hidden N=2 supergroup invariance and links to deformed Heisenberg algebra.

Findings

Model exhibits hidden N=2 Poincaré supergroup symmetry.

Quantum states form a supersymmetric doublet of fractional spin particles.

Quantum space embeds into Fock space of a deformed harmonic oscillator.

Abstract

We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model introduced possesses hidden invariance under N=2 Poincar\'e supergroup with a central charge saturating the BPS bound. At the classical level the model admits a Hamiltonian formulation with two first class constraints on the phase space $T^*(R^{1,2})\times {\cal L}^{1|1}$, where the K\"ahler supermanifold ${\cal L}^{1|1}\cong OSp(2|2)/U(1|1)$ is a minimal superextension of the Lobachevsky plane. The model is quantized by combining the geometric quantization on ${\cal L}^{1|1}$ and the Dirac quantization with respect to the first class constraints. The constructed quantum theory describes a supersymmetric doublet of fractional spin particles. The space of quantum superparticle states with a fixed momentum is embedded into the Fock space of a deformed harmonic oscillator.