R-deformed Heisenberg algebra

Abstract

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.

11 pages, LaTeX

Cited by in corpus (15)

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• Hidden nonlinear supersymmetries in pure parabosonic systems
• Bosons, fermions and anyons in the plane, and supersymmetry
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• Fractional supersymmetry and hierarchy of shape invariant potentials
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• Three-dimensional fractional-spin gravity
• N=1, D=3 Superanyons, osp(2|2) and the Deformed Heisenberg Algebra
• Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum
• Non-Hermitian Oscillator and R-deformed Heisenberg Algebra
• Time-dependent Dunkl-Pauli Oscillator
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases
• Hidden supersymmetry and Berezin quantization of N=2, D=3 spinning superparticles
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications
• Universality of the R-deformed Heisenberg algebra