Dvooscilatorni i modeli tipa slobodne čestice u kosmologiji
AuthorRadovančević, Darko V.
MentorNešić, Ljubiša D.
Committee membersĐorđević, Goran S.
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The theme of this PhD thesis is related to the study of minisuperspace cosmological models whose Lagrangians can be reduced to Lagrangian of the free relativistic particle or to Lagrangian of the two oscillators of the same or dierent frequencies. After getting acquainted with the elements of p-adic and adelic mathematical analysis and quantum mechanics, classical and quantum cosmology, the thesis discusses the aforementioned cosmological models in classic, p-adic noncommutative approach. The study of cosmological models within the p-adic noncommutative formalism is of particular importance because both of these approaches suggest discreteness of the structure of space-time at the Planck scale which is associated with the mechanism of signature transition within Hartl-Hawking boundary condition. After considering Milne model, in the classic section, rstly the classication of the two-oscillator models according to the form of Lagrangian is performed, concrete examples are g...iven and then their Hamiltonians and classical actions are determined. The questions of the Hamiltonian condition and classical signature transition are especially considered. In the p-adic part, quantum p-adic and adelic forms of these models are presented and the conditions of the existence of their vacuum p-adic states are determined. After that noncommutative forms of the models are considered and their classical noncommutative actions and propagators are determined. In addition to a better understanding of the early stages of the universe evolution, the study of these models will provide a better insight into the dynamics and thermodynamics of the interior of non-charged and non-rotating (Schwarzschild) black hole whose Einstein- -Hilbert action can be reduced to action one of the two-oscillator cosmological model (which will be discussed in the eighth chapter of the thesis). The original results presented in this thesis are of interest for further study of the black holes, the early evolution of the universe and further research in the eld of quantum gravitation in general.