$q$-Deformed Classical Lie Algebras and their Anyonic Realization

Details $q$-Deformed Classical Lie Algebras and their Anyonic Realization $q$-Deformed Classical Lie Algebras and their Anyonic Realization

1993-04-23

arxiv.org/abs/hep-th/9304108v1

J.Phys.A27:801-816,1994

Physics

High Energy Physics

High Energy Physics - Theory

in Plain TeX; one figure and two tables in LaTeX are not included but available under request , 22 pages, DFTT 16/93

Scientific paper

10.1088/0305-4470/27/3/022

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 $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter $q$ 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 $q$ can also be real.

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