Hilbert Spaces for Nonrelativistic and Relativistic "Free" Plektons (Particles with Braid Group Statistics)

Abstract

Using the theory of fibre bundles, we provide several equivalent intrinsic descriptions for the Hilbert spaces of $n$ ``free'' nonrelativistic and relativistic plektons in two space dimensions. These spaces carry a ray representation of the Galilei group and a unitary representation of the Poincaré group respectively. In the relativistic case we also discuss the situation where the braid group is replaced by the ribbon braid group.

26 pages, standard LaTeX, 3 figures on request. An error in the appendix has been corrected, thanks to D.R.Grigore

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