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Information × Registration Number 0212U006267, 0106U007885 , R & D reports Title Methods of theory of symmetry and the problems of non-linear dynamics in modern field theory and in the theory of elementary particles popup.stage_title Head Gavrilik Oleksandr Mykhailovych, Registration Date 12-03-2012 Organization Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine popup.description2 The report is based on 97 scientific papers, made in the department during 2007-2011 and published in monograph and leading national and international scientific journals. This research is devoted to study of a number of problems in the theory of nonlinear quantum oscillators, classical and quantum integrable systems, renormalization, categorical and topological aspects of quantum feild theories. New models, including multiparametric ones, of deformed (nonlinear) quantum oscillators are constructed, and their basic properties studied (classification of representations, Hopf structure, spectra of observable operators, coherent states). Some physical applications to models of quantum optics and generalized models of Bose gas are proposed. Deformed analogs of Bose gas model are developed, in which some correlation functions and thermodynamic quantities are obtained. It is proved that composite bosons (twofermiion composites) are realizable in terms of deformed oscillators of certain form. A number of results are obtained for existing and new quantum integrable systems of statistical physics, quantum optics and theory of magnetism; generalizations of model of BCS and Goudin are found, as well as of Bose-Hubbard dimer model and Jaynes-Cummings-Dicke model. Quantum spin chain with biquadratic exchange interaction is studied. Explicit formulas for form factors and correlation functions in two-dimensional Ising model, Potts quantum chain, quantum XY-chain in a transverse magnetic field are derived. An interesting results on the actual issues of physics of strong interacting matter at ultra high energy density, as well as renormalization, topological and categorical aspects of quantum field systems are obtained. Product Description popup.authors І.М. Бурбан А.В. Козак А.В. Назаренко А.М. Павлюк А.П. Ребеш В.І. Кучерявий М.З. Іоргов О.М. Гаврилик Т.В. Скрипник Ю.В. Тихий Ю.М. Беспалов popup.nrat_date 2020-04-02 Close