Intrinsic anyonic spin through deformed geometry

Abstract

The properties of the deformed bosonic oscillator, and the quantum groups ${\mathcal{U}}_q(SL(2))$ and $G{L}_q(2)$ in the limit as their deformation parameter $q$ goes to a root of unity are investigated and interpreted physically. These properties are seen to be related to fractional supersymmetry and intrinsic anyonic spin. A simple deformation of the Klein-Gordon equation is introduced, based on $G{L}_q(2)$. When $q$ is a root of unity this equation is a root of the undeformed Klein-Gordon equation.

26 pages, LaTeX

References in corpus (1)

• Geometrical foundations of fractional supersymmetry

Cited by in corpus (6)

• Geometrical foundations of fractional supersymmetry
• Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case
• Fractional spin through quatum (super)Virasoro algebras
• Fractional Supersymmetry and F-fold Lie Superalgebras
• Fractional spin through quantum strange superalgebra ${\tilde{P}}_Q(n)$
• Fractional Spin through Quantum Affine Algebra $\hat{A}(n)$ and quantum affine superalgebra $\hat{A}(n,m)$