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Information × Registration Number 0214U003650, 0111U002295 , R & D reports Title Symmetries theory methods and their applications in quantum physics popup.stage_title Head Kachuryk Ivan Ivanovich, Registration Date 11-02-2014 Organization Khmelnytskiy National University popup.description2 Object of study - symmetry models quantum mechanical systems, theory and physical applications. Objective - design and development algebraically -group ( symmetry ) techniques and their subsequent use in quantum physics. Research methods - algebraic approach to the study and algebraic structures arising explicit in describing the symmetries of quantum oscillators. The theory of higher symmetry groups (SO (n), SU (n), U (n), Sp (n) SL (n, R), Gl (n, R), SO (n, C)) and obtain the infinitesimal operator for some classes of representations of these groups in the canonical and non-canonical bases, which correspond to the reduction of these groups are compact and non-compact subgroups , respectively. Built some new models deformed quantum oscillators, which would lead to asymmetric boundary classical oscillator found in these models of the position . The structure of algebra and new models of deformed oscillators and found a criterion for their classification. Get the modified value for the oscillator Tamm - Dankoff , Properties unconventionally deformed oscillators of type m- oscillator Yanusisa . The method of classical invariant theory to the study of algebraic structures arising explicit in describing the symmetries of quantum oscillators , calculated Poincar? series of algebras of invariants and developed an analog theoretic method for finding invariant kernels of locally nilpotent linear dyferentsiyuvan . The results are of theoretical research and can be used in quantum field theory, the theory of invariants, noncommutative algebra Product Description popup.authors Бедратюк Леонід Петрович Гаврилик Олександр Миколайович Качурик Iван Iванович popup.nrat_date 2020-04-02 Close