Non-Trivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons

de Traubenberg, M. Rausch; Slupinski, M. J.

Non-Trivial Extensions of the 3D-Poincaré Algebra and Fractional Supersymmetry for Anyons

Authors

Description

Non-trivial extensions of the three dimensional Poincaré algebra, beyond the supersymmetric one, are explicitly constructed. These algebraic structures are the natural three dimensional generalizations of fractional supersymmetry of order $F$ already considered in one and two dimensions. Representations of these algebras are exhibited, and unitarity is explicitly checked. It is then shown that these extensions generate symmetries which connect fractional spin states or anyons. Finally, a natural classification arises according to the decomposition of $F$ into its product of prime numbers leading to sub-systems with smaller symmetries.
17 pages, LaTex, the algebraic structure is given with more details, unitarity of the respresentation is explicitly checked, references has been added, one author has been added, to appear in Mod. Phys. Lett. A