1994/07/25 by Marialuisa Frau, M. Frau, A. Lerda +6
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9407161
Lectures given at the Varenna School on ``Quantum Groups and Their Applications in Physics'' (June 1994), DFTT 33/94 and DFT-US 2/94, 31 pp. (5 figures and 1 table on request) LaTex file (the macro subeqn.sty is appended at the end the LaTex file)
arxiv created 1994/07/25 · openalex publication_date 1994/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.