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The quantum theory of gravity has eluded physicists for many decades. The apparent contradiction between the physics describing the microscopic and the macroscopic regimes has given rise to some beautiful theories and mathematics. In this paper, we discuss some aspects of one of those theories, namely loop quantum gravity (LQG). Specifically, we discuss the discreteness of spacetime, a feature that distinguishes LQG from some of the other contending theories. After a general discussion in the introduction, we discuss the dynamics and quantization of the simplices (tetrahedra) that make up the space. The discrete geometry of these tetrahedral grains of space has some beautiful physical and mathematical properties. We use semiclassical physics and some classical results in algebraic geometry and topology to investigate many of these properties.
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Antu, Santanu B., "Geometry and Semiclassics of Tetrahedral Grain of Space" (2023). Senior Projects Spring 2023. 49.
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