13 research outputs found
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.Comment: 11 pages, typos correcte
Super-extended noncommutative Landau problem and conformal symmetry
A supersymmetric spin-1/2 particle in the noncommutative plane, subject to an
arbitrary magnetic field, is considered, with particular attention paid to the
homogeneous case. The system has three different phases, depending on the
magnetic field. Due to supersymmetry, the boundary critical phase which
separates the sub- and super-critical cases can be viewed as a reduction to the
zero-energy eigensubspace. In the sub-critical phase the system is described by
the superextension of exotic Newton-Hooke symmetry, combined with the conformal
so(2,1) ~ su(1,1) symmetry; the latter is changed into so(3) ~ su(2) in the
super-critical phase. In the critical phase the spin degrees of freedom are
frozen and supersymmetry disappears.Comment: 12 pages, references added, published versio
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 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 Inonu-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 the supersymmetric cases.Comment: 54 pages. Typos corrected, refs updated. Published versio