Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons

TL;DR

This paper explores the supersymmetric properties of a spin-1/2 particle in a magnetic vortex field, revealing specific self-adjoint extensions, superalgebra structures, and applications to anyon models with supersymmetry.

Contribution

It identifies two compatible self-adjoint Hamiltonian extensions in a magnetic vortex field that preserve N=2 supersymmetry and introduces a tri-supersymmetry framework with superconformal structures.

Findings

Two self-adjoint extensions compatible with N=2 supersymmetry are identified.

A tri-supersymmetry framework with nonlocal integrals of motion is developed.

Application to anyon models reveals supersymmetric contact interactions.

Abstract

The quantum nonrelativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N=2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two self-adjoint extensions of the Hamiltonian that are compatible with the standard N=2 supersymmetry. We show that only in these two cases one of the subsystems coincides with the original spinless Aharonov-Bohm model and comes accompanied by the super-partner Hamiltonian which allows a singular behavior of the wave functions. We find a family of additional, nonlocal integrals of motion and treat them together with local supercharges in the unifying framework of the tri-supersymmetry. The inclusion of the dynamical conformal symmetries leads to an infinitely generated superalgebra, that contains several representations of the superconformal osp(2|2) symmetry. We present the application of the results in the framework of the two-body model of identical anyons. The nontrivial contact interaction and the emerging N=2 linear and nonlinear supersymmetries of the anyons are discussed.