Where Do Braid Statistics and Discrete Motion Meet Each Other?

DOI

10.2991/jnmp.2008.15.s3.34How to use a DOI?

Abstract

We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We focus on the discrete equations which take place in the case of generalized exclusion principle statistics. We show that their exact solutions are quantum dimensions of the irreducible representations of certain quantum group. These solutions provide an example of the point where the generalized exclusion principle statistics and braid statistics meet each other. We propose a procedure to construct the quantum dimer models by means of projection of the knotted field configurations that involved braiding features of one-dimensional topology.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Luigi Martina
AU  - Alexander Protogenov
AU  - Valery Verbus
PY  - 2008
DA  - 2008/10/01
TI  - Where Do Braid Statistics and Discrete Motion Meet Each Other?
JO  - Journal of Nonlinear Mathematical Physics
SP  - 353
EP  - 361
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.34
DO  - 10.2991/jnmp.2008.15.s3.34
ID  - Martina2008
ER  -