Anyons and Deformed Lie Algebras

Details Anyons and Deformed Lie Algebras Anyons and Deformed Lie Algebras

1994-07-25

arxiv.org/abs/hep-th/9407161v1

Physics

High Energy Physics

High Energy Physics - Theory

Lectures given at the Varenna School on ``Quantum Groups and Their Applications in Physics'' (June 1994), DFTT 33/94 and DFT-U

Scientific paper

We discuss the connection between anyons (particles with fractional statistics) and deformed Lie algebras (quantum groups). After a brief review of the main properties of anyons, we present the details of the anyonic realization of all deformed classical Lie algebras in terms of anyonic oscillators. The deformation parameter of the quantum groups is directly related to the statistics parameter of the anyons. Such a realization is a direct generalization of the Schwinger construction in terms of fermions and is based on a sort of bosonization formula which yields the generators of the deformed algebra in terms of the undeformed ones. The entire procedure is well defined on two-dimensional lattices, but it can be consistently reduced also to one-dimensional chains.

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