Topological Regularisation of Quantum Gravity and Derivation of the Standard Model as an Effective Low Energy Theory in Discrete Geometric Physics
Year: 2026
Type: article
Abstract: This work demonstrates that the Oh‑topos and the bounce mechanism of Discrete Geometric Physics (DGP) naturally give rise to the gauge group SU(3)×SU(2)×U(1)SU(3)×SU(2)×U(1) and provide a topological regularisation of quantum gravity, eliminating all singularities. All gauge coupling constants are derived from the geometry of the 26‑vertex cubic lattice and, after renormalisation group running using the lattice block‑spin procedure, agree with PDG values at the MZMZ scale to within 0.2%. Key results: 1. Gauge group derivation: o 7 left‑handed spiral contours generate the linking matrix. o Eigenvalues: λ1=−1λ1=−1 (multiplicity 1), λ2=3/4λ2=3/4 (multiplicity 6). o Lie algebra: su(3)⊕su(2)⊕u(1)su(3)⊕su(2)⊕u(1). 2. Gauge coupling constants at the Planck scale: gs=π7≈0.4488,g=π72≈0.3174,g′=π143≈0.1295.gs=7π≈0.4488,g=72π≈0.3174,g′=143π≈0.1295. 3. Comparison with PDG after renormalisation group running: Constant DGP (at MZMZ) PDG (MZMZ) Deviation αsαs 0.1181 0.1179 0.2% αα 1/137.036 1/137.036 <0.01% sin2θWsin2θW 0.2312 0.2312 <0.01% 4. Higgs boson mass: o Derived from minimisation of the potential V(J)V(J) on the lattice. o mH≈125.1 GeVmH≈125.1GeV (agrees with PDG 125.10±0.14 GeV125.10±0.14GeV). 5. Regularisation of quantum gravity: o Bounce condition J≥Jcrit=0.01J≥Jcrit=0.01 ensures bounded curvature. o Replaces the Big Bang singularity with a Big Bounce. o Effective action: S=∫(R/(16πGeff)+LSM)−g d4xS=∫(R/(16πGeff)+LSM)−gd4x. This revised version includes: · Explicit cross‑references to Volume 1, Chapters 3 and 7. · Expanded derivation of gauge coupling constants. · Full alignment with the bounce mechanism from the base theory. · Scale‑dependent effective gravitational constant: Geff(N)=G⋅22(116−N)Geff(N)=G⋅22(116−N).
Author: Ivan Davidenko
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166330485