161 research outputs found

### R-deformed Heisenberg algebra, anyons and d=2+1 supersymmetry

A universal minimal spinor set of linear differential equations describing
anyons and ordinary integer and half-integer spin fields is constructed with
the help of deformed Heisenberg algebra with reflection. The construction is
generalized to some d=2+1 supersymmetric field systems. Quadratic and linear
forms of action functionals are found for the universal minimal as well as for
supersymmetric spinor sets of equations. A possibility of constructing a
universal classical mechanical model for d=2+1 spin systems is discussed.Comment: 11 pages, LaTe

### R-deformed Heisenberg algebra

It is shown that the deformed Heisenberg algebra involving the reflection
operator R (R-deformed Heisenberg algebra) has finite-dimensional
representations which are equivalent to representations of paragrassmann
algebra with a special differentiation operator. Guon-like form of the algebra,
related to the generalized statistics, is found. Some applications of revealed
representations of the R-deformed Heisenberg algebra are discussed in the
context of OSp(2|2) supersymmetry. It is shown that these representations can
be employed for realizing (2+1)-dimensional supersymmetry. They give also a
possibility to construct a universal spinor set of linear differential
equations describing either fractional spin fields (anyons) or ordinary integer
and half-integer spin fields in 2+1 dimensions.Comment: 11 pages, LaTe

### 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$\vert$2) 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.Comment: 21 pages, LaTe

### Deformed Heisenberg Algebra with Reflection, Anyons and Supersymmetry of Parabosons

Deformed Heisenberg algebra with reflection appeared in the context of
Wigner's generalized quantization schemes underlying the concept of parafields
and parastatistics of Green, Volkov, Greenberg and Messiah. We review the
application of this algebra for the universal description of ordinary spin-$j$
and anyon fields in 2+1 dimensions, and discuss the intimate relation between
parastatistics and supersymmetry.Comment: 4 pages. Talk given at the Int. Conf. ``Spin-Statistics Connection
and Commutation Relations", Anacapri, Capri Island, Italy -- May 31-June 3,
2000 (to appear in Proceedings

- â€¦