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

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

1993-10-08

arxiv.org/abs/hep-th/9310054v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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 Poincar\'{e} group respectively. In the relativistic case we also discuss the situation where the braid group is replaced by the ribbon braid group.

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