Hyperoctahedral Symmetry Breaking and Recovery in Lattice QCD — E8 Intelligence Research

FINDING: Lattice QCD replaces continuous Lorentz symmetry with the hyperoctahedral group (B₄), the finite crystallographic point group of the 4D hypercube, breaking Lorentz invariance at the lattice scale while recovering it in the continuum limit. | MATH: The hyperoctahedral group B₄ has order |B₄| = 2⁴·4! = 384. Its irreducible representations classify lattice baryon operators; continuum spin J states decompose into B₄ irreps (e.g., J=1/2 → H₄⊕H₅; J=3/2 → H₆⊕H₇⊕H₈, where Hᵢ are the 5 irreps of B₄ of dimensions 1,1,2,3,3,4,4,4,4,8,8,8,8,16,16,16,16 — total 20 irreps). The lattice spacing a acts as a regulator; Lorentz invariance is recovered as a→0 with renormalized couplings. Spontaneous Lorentz breaking in QED₃ involves a Chern–Simons term generating a parity-odd mass, with critical exponents from ERG flow. | CONNECTION: B₄ is the Weyl group of the D₄ root system (the 4D hypercube/16-cell), whose Coxeter number is 8. The ratio of the lattice spacing to the physical correlation lengt Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com