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

Journal Article · Wed Dec 15 00:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.06.005· OSTI ID:21457139

Correa, Francisco ^[1]; Falomir, Horacio ^[2]; Jakubsky, Vit ^[3]

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1. Centro de Estudios Cientificos (CECS), Valdivia (Chile)
2. IFLP/CONICET - Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900) La Plata (Argentina)
3. Nuclear Physics Institute, ASCR, 250 68 Rez (Czech Republic)

The quantum non-relativistic 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 vertical bar 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.

• OSTI ID: 21457139
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 12; Other Information: DOI: 10.1016/j.aop.2010.06.005; PII: S0003-4916(10)00112-0; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AHARONOV-BOHM EFFECT
ANYONS
CONFORMAL INVARIANCE
FERMIONS
HAMILTONIANS
MAGNETIC FIELDS
NONLINEAR PROBLEMS
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SPIN
SUPERSYMMETRY
TWO-BODY PROBLEM
VORTICES
WAVE FUNCTIONS
ANGULAR MOMENTUM
ENERGY RANGE
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
PARTICLE PROPERTIES
QUANTUM OPERATORS
QUASI PARTICLES
SYMMETRY