Multidimensional Universe Model and Quantum Mechanical Applications
This study investigates quantum mechanical applications in a D ≥ 4 multidimensional universemodel and shows its mathematical background. The theoretical structure is discussed aboutcorrelation function, density matrices, Feynman path integral, Bell’s inequality, and covariantSchrödinger-Dirac equations. Each structure has been redefined using Riemann geometry andtopological tools.Correlation function ϵ(p, q) explains entanglement with phase difference and metric distance.Feynman path integral has been redefined and generalized consistently with this structure. TheSchrödinger and Dirac equations have been made covariant in curved space-time and becamemultidimensional with using Laplace-Beltrami and spin connections. Through von Neumannentropy, entanglement has been measurable in higher dimensional systems and it has beenshown that the violation conditions of Bell’s inequality depend on phase difference and metricdistance.Topologically when we define the phase function as ϕ : M → S1, the protection of the windingnumbers ensures the long range stability of correlations. This study presents a formulationthat is consistent in both theoretical and experimental contexts.
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