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The quantum tetrahedron and the length spectrum
Preview AbstractA new independent approach to the granularity of space is derived. The Bohr–Sommerfeld length spectrum is computed and discussed. Some values of the spectrum are given and compared with those found canonically elsewhere.
Loop gravity and Schwarzschild spacetime
Preview AbstractA discretization for the Schwarzschild spacetime manifold is introduced and investigated. It is shown that the discreteness of the area of space shown in loop gravity leads to a tetrahedral structure characterizing the Schwarzschild manifold.
The quantum polyhedra and the volume spectrum
Preview AbstractThe Bohr–Sommerfeld volume spectrum of polyhedron with arbitrary number of faces is computed. Some spacial cases (the three, four and five valent node Hilbert space) are studied.