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