Simplicial Lattice Field Theory (Vol I): The Lorentzian Metric from D4 Lattice Frustration
Simplicial Lattice Field Theory (Vol I): The Lorentzian Metric from D4 Lattice Frustration
We construct a discrete vacuum from the D4 root lattice with unit cell the 24-cell. Topological frustration breaks O(4) to O(1,3), producing the Lorentzian signature. The frustration angle arctan(2) is derived from the virial theorem. SO(8) triality provides exactly three fermion sectors. Two free parameters (lattice spacing a and tension τ) fix all dimensional scales.
simplicial lattice field theory, 24-cell, D4 root lattice, Hodge decomposition, discrete gauge theory, lattice gauge theory, fine-structure constant, Weinberg angle, Higgs mass, proton-electron mass ratio, CKM matrix, PMNS matrix, neutrino mixing, color confinement, baryon number, cosmological constant, dark matter, dark energy, holographic principle, Kaplan-Yorke dimension
simplicial lattice field theory, 24-cell, D4 root lattice, Hodge decomposition, discrete gauge theory, lattice gauge theory, fine-structure constant, Weinberg angle, Higgs mass, proton-electron mass ratio, CKM matrix, PMNS matrix, neutrino mixing, color confinement, baryon number, cosmological constant, dark matter, dark energy, holographic principle, Kaplan-Yorke dimension
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