QUANTUM GROUP SIGMA-MODELS

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 non-commutative 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(N) = 1, in which case quantum matrices U(q)(2) are realised as 2N x 2N unitary matrices. Open problems are pointed out.