Anyons as spinning particles

A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are investigated. The relationship between all the known approaches to anyons as spinning particles is established. Some widespread misleading notions on the general properties of (2+1)-dimensional anyons are removed.Comment: 29 pages, LaTeX, a few corrections and references added; to appear in Int. J. Mod. Phys.

Linear Differential Equations for a Fractional Spin Field

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional nonunitary representations of that group, $0<2j\in Z$, they are transformed into equations for spin-$j$ fields. A local gauge symmetry associated to the vector system of equations is identified and the simplest gauge invariant field action, leading to these equations, is constructed.Comment: 15 pages, LATEX, revised version of the preprint DFTUZ/92/24 (to be published in J. Math. Phys.

Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions

Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), [a^{-},a^{+}]=1+\nu K, involving the Klein operator K, \{K,a^{\pm}\}=0, K^{2}=1. The connection of the minimal set of equations with the earlier proposed `universal' vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of exact and spontaneously broken N=2 supersymmetry allowing us to realize a Bose-Fermi transformation and spin-1/2 representation of SU(2) group in terms of one bosonic oscillator. The construction admits an extension to the case of OSp(2\vert2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. A possibility of `superimposing' the two applications of the DHA for constructing a supersymmetric (2+1)-dimensional anyon system is discussed. As a consequential result we point out that osp(2|2) superalgebra is realizable as an operator algebra for a quantum mechanical 2-body (nonsupersymmetric) Calogero model

Hamiltonian Frenet-Serret dynamics

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the Hamiltonian equations of motion are written down and a geometrical interpretation is provided for the canonical variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class. Quant. Gra

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

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.Comment: 23 pages, Late