Anyons and quantum groups. (English) Zbl 0906.17004
Summary: Anyonic oscillators with fractional statistics are built on a two-dimensional square lattice by means of a generalized Jordan-Wigner construction, and their deformed commutation relations are thoroughly discussed. Such anyonic oscillators, which are non-local objects that must not be confused with \(q\)-oscillators, are then combined à la Schwinger to construct the generators of the quantum group \(SU(2)_q\) with \(q=\exp(i\pi\nu)\), where \(\nu\) is the anyonic statistical parameter.
MSC:
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
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