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Published August 21, 2025 | Version v1
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Multidimensional Universe Model and Quantum Mechanical Applications

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Description

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

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Dates

Created
2025-08-21

References

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