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Information × Registration Number 0221U104094, 0116U007065 , R & D reports Title Research of classical and quantum symmetries in the theoretical-field and string models and problems of statistical mechanics of the condensed media popup.stage_title Head Slyusarenko Yurii Viktorovich, Доктор фізико-математичних наук Registration Date 02-03-2021 Organization National Science Center "Kharkiv Institute of Physics and Technology" popup.description2  There has been established the correspondence between the geometric structure of non-linearities in the theory of extended relativistic objects – p-branes and non-linearities in the theories of gravitation and non-Abeliean gauge fields. It has been shown that geometric nature of non-linearities in the brane theory reveals itself upon transition to formulations of their Lagrangians in terms of generalized coordinates realized by the coefficients of the first and second fundamental forms of world hypersurfaces. There has been given physical interpretation of these generalized coordinates as Nambu-Goldstone tensor fields related to spontaneous breaking of the Poincare symmetry of Minkowski space-time upon embedding in it of brane hypersurfaces. There has been constructed non-linear invariant interaction potential of these tensor fields and examined its extremals that turn out to be saddle hypersurfaces indicating the presence of unstable vacuum states in the brane theory. It has been shown that vacuum instability could play a role of the physical mechanism for inflation triggering with subsequent reheating of the early Universe modelled by 4-dimensional hypersurface of 3-brane embedded into 5-dimensional space-time. There has been proposed novel model of the spinning particle in anti-de Sitter space-time realized as a real projective manifold parametrized by the uniform coordinates. There have obtained Hamiltonian constraints of the model and constructed it Lagrange and Hamilton functions, proved classical integrability of it Lagrangian equations. It has been shown that quantization of the model leads to the Dirac equation for particle with spin 1/2 , for which various representations were obtained. There have been considered gauge-invariant interactions of the spinning particle with external electromagnetic and antisymmetric tensor fields. Product Description popup.authors popup.nrat_date 2021-03-02 Close