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arXiv · hep-th/9204086

Quantum Group $σ$ Models

Y. Frishman·J. Lukierski·W. J. Zakrzewski
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Abstract

Field-theoretic models for fields taking values in quantum groups are investigated. First we consider $SU_q(2)$ $σ$ model ($q$ real) expressed in terms of basic notions of noncommutative differential geometry. We discuss the case in which the $σ$ models fields are represented as products of conventional $σ$ fields and of the coordinate-independent algebra. An explicit example is provided by the $U_q(2)$ $σ$ 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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Y. Frishman, J. Lukierski, W. J. Zakrzewski. 1992-04-27. Quantum Group $σ$ Models. https://doi.org/10.1088/0305-4470%2F26%2F2%2F017

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