Bosons, fermions and anyons in the plane, and supersymmetry
- Laboratoire de Mathematiques et de Physique Theorique, Unite Mixte de Recherche 6083 du CNRS, Federation Denis Poisson, Universite de Tours, Parc de Grandmont, F-37200 Tours (France)
Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on non-unitary infinite-dimensional half-bounded representations of the (2 + 1)D Lorentz algebra is revealed. Those associated with non-unitary representations interpolate between bosons and fermions. The extended formulation of the theory includes the previously known Jackiw-Nair (JN) and Majorana-Dirac (MD) descriptions of anyons as particular cases, and allows us to compose bosons and fermions from entangled anyons. The theory admits a simple supersymmetric generalization, in which the JN and MD systems are unified in N = 1 and N = 2 supermultiplets. Two different non-relativistic limits of the theory are investigated. The usual one generalizes Levy-Leblond's spin 1/2 theory to arbitrary spin, as well as to anyons. The second, 'Jackiw-Nair' limit (that corresponds to Inoenue-Wigner contraction with both anyon spin and light velocity going to infinity), is generalized to boson/fermion fields and interpolating anyons. The resulting exotic Galilei symmetry is studied in both the non-supersymmetric and supersymmetric cases.
- OSTI ID:
- 21457146
- Journal Information:
- Annals of Physics (New York), Vol. 325, Issue 9; Other Information: DOI: 10.1016/j.aop.2010.02.007; PII: S0003-4916(10)00039-4; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ANYONS
BOSONS
FERMIONS
NONUNITARY REPRESENTATIONS
QUANTUM ENTANGLEMENT
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SPIN
SUPERMULTIPLETS
SUPERSYMMETRY
VECTORS
VISIBLE RADIATION
WAVE EQUATIONS
ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC RADIATION
ENERGY RANGE
EQUATIONS
FIELD THEORIES
MATHEMATICS
MULTIPLETS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUASI PARTICLES
RADIATIONS
SYMMETRY
TENSORS