Quantum group sigma models

Abstract

Field-theoretic models for fields taking values in quantum groups are investigated. First the authors consider the SUq(2) sigma model (q real) expressed in terms of basic notions of noncommutative differential geometry. They discuss the case in which the sigma model fields are represented as products of conventional sigma fields and of the coordinate-independent algebra. An explicit example is provided by the Uq(2) sigma model with qN=1, in which case quantum matrices Uq(2) are realized as 2N*2N unitary matrices. Open problems are pointed out.