Gavrilik A. 3. Representations and realizations of quantum and classical groups in quantum systems of fields and particles

The dissertation is devoted to the investigation of representations of noncompact groups, quantum algebras, their application in hadron physics and quantum gravity, to the study of the renormalization group properties of the nonlinear sigma models on the nonsymmetric coset spaces. Representations of the noncompact Lie groups related with N=6 supergravity are explored. The representations of pseudounitary groups are utilized in the treatment of hadron masses and analysis of mass formulas. New q-deformations of the Lie algebras of the orthogonal and euclidean groups are introduced, the analysis of their representations and role in quantum gravity is given. Quantum pseudounitary groups are applied within new approach to flavour symmetries of hadrons, new mesonic and baryonic mass formulas are derived, topological description of quark flavours and the connection of deformation parameter to the Cabibbo angle is found out. New string compactifications, as well as the scaling behaviour of the Stiefel nonlinear sigma models, are studied.