Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems |

D. JacakInstitute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland L. Jacak and K. WieczorekInstitute of Physics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland |

Received: June 7, 1993 |

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The problem of the non-standard statistics for one-, two- and three-dimensional systems of N identical particles on various manifolds is reviewed in terms of the braid group theory. The braid groups together with their unitary representations are studied for the line, circle, plane, sphere, torus and the three-dimensional Euclidean space. Nonequivalent quantizations of several physical systems are presented. |

DOI: 10.12693/APhysPolA.85.483 PACS numbers: 03.65.Bz, 05.30.-d |