Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons

A novel BRST approach in generalizing the Jackiw-Nair anyon

A novel BRST quantization is described, which is applied in generalizing the Jackiw-Nair construction of anyon. We have explicitly shown that the matter states connected to an unconventional ("non-zero") BRST ghost sector are physical. They are identified to the Jackiw-Nair system in a particular gauge. Also for the first time an indepth analysis of the present kind for a reducible constraint system, ( where the constraints are not independent), has been performed.

相对论性 Jackiw-Nair 任意子的不确定性关系：第一性原理推导

Uncertainty Relations for the Relativistic Jackiw-Nair Anyon: A First Principles Derivation

本文从第一性原理出发，在纯量子力学框架中推导了相对论性 Jackiw-Nair 任意子的位置-位置和位置-动量不确定性关系，通过非平凡的位置不确定性支持任意子生活在二维非对易空间，并证明同一形式体系用于电子时得到平凡结果，从而与三维对易空间一致。

Anyon wave equations and the noncommutative plane

The ``Jackiw-Nair'' non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Levy-Leblond type for the ``exotic'' particle, associated with the two-fold central extension of the planar Galilei group. An infinite dimensional representation of the Galilei group is found. The velocity operator is studied, and the observable coordinates describing a noncommutative plane are identified.

Bosons, fermions and anyons in the plane, and supersymmetry

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 c…

Bosonized supersymmetry of anyons and supersymmetric exotic particle on the non-commutative plane

A covariant set of linear differential field equations, describing an N=1 supersymmetric anyon system in (2+1)D, is proposed in terms of Wigner's deformation of the bosonic Heisenberg algebra. The non-relativistic ``Jackiw-Nair'' limit extracts the ordinary bosonic and fermionic degrees of freedom from the Heisenberg-Wigner algebra. It yields first-order, non-relativistic wave equations for a spinning particle on the non-commutative plane that admits a Galilean exotic planar N=1 supersymmetry.

Spin and exotic Galilean symmetry

A slightly modified and regularized version of the non-relativistic limit of the relativistic anyon model considered by Jackiw and Nair yields particles associated with the twofold central extension of the Galilei group, with independent spin and exotic structure.