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

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

1996-09-25

arxiv.org/abs/hep-th/9609203v2

Mod.Phys.Lett.A12:3051-3066,1997

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, LaTex, the algebraic structure is given with more details, unitarity of the respresentation is explicitly checked, r

Scientific paper

10.1142/S0217732397003174

Non-trivial extensions of the three dimensional Poincar\'e 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.

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