The Mass Gap of the Space-time and its Shape

Abstract

Snyder's quantum space-time which is Lorentz invariant is investigated. It is found that the quanta of space-time have a positive mass that is interpreted as a positive real mass gap of space-time. This mass gap is related to the minimal length of measurement which is provided by Snyder's algebra. Several reasons to consider the space-time quanta as a 24-cell are discussed. Geometric reasons include its self-duality property and its 24 vertices that may represent the standard model of elementary particles. The 24-cell symmetry group is the Weyl/Coxeter group of the $F_4$ group which was found recently to generate the gauge group of the standard model. It is found that 24-cell may provide a geometric interpretation of the mass generation, Avogadro number, color confinement, and the flatness of the observable universe. The phenomenology and consistency with measurements is discussed.

14 pages, two figures, revtex4, Published in Fortschritte der Physik - Progress of Physics

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• Universality of Quantum Gravity Corrections
• Minimum Length Cutoff in Inflation and Uniqueness of the Action
• Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra
• Division algebraic symmetry breaking
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Universality of minimal length
• Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

Cited by in corpus (2)

• Graviton mass due to dark energy as a superconducting medium: theoretical and phenomenological aspects
• Quantum Spacetime Imprints: The 24-Cell, Standard Model Symmetry and Its Flavor Mixing