$q$-Deformed Classical Lie Algebras and their Anyonic Realization
High Energy Physics - Theory
2011-07-21 v1
Abstract
All classical Lie algebras can be realized \`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their -deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter is a phase related to the anyonic statistical parameter. A crucial r\^ole in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case can also be real.
Cite
@article{arxiv.hep-th/9304108,
title = {$q$-Deformed Classical Lie Algebras and their Anyonic Realization},
author = {Marialuisa Frau and Marco A. R-Monteiro and Stefano Sciuto},
journal= {arXiv preprint arXiv:hep-th/9304108},
year = {2011}
}
Comments
in Plain TeX; one figure and two tables in LaTeX are not included but available under request , 22 pages, DFTT 16/93