Quantum Group $σ$ Models

Details Quantum Group $σ$ Models Quantum Group $σ$ Models

1992-04-27

arxiv.org/abs/hep-th/9204086v1

J.Phys. A26 (1993) 301-312

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

10.1088/0305-4470/26/2/017

Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $\sigma$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in which the $\sigma$ models fields are represented as products of conventional $\sigma$ fields and of the coordinate-independent algebra. An explicit example is provided by the $U_q(2)$ $\sigma$ model with $q\sp{N}=1$, in which case quantum matrices $U_q(2)$ are realised as $2N\times 2N$ unitary matrices. Open problems are pointed out.

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