Lattice QCD Baryon Operators: From SO(3) Spin to Octahedral Group Irreps — E8 Intelligence Research

FINDING: Lattice QCD baryon operators require explicit reduction from continuum SO(3) rotational symmetry to the finite octahedral group (O_h) of the cubic lattice, with operator construction guided by irreducible representations (irreps) of O_h rather than spin-J of SO(3). | MATH: Continuum spin-J decomposes under O_h as: J=0→A1; J=1→T1; J=2→E⊕T2; J=3→A2⊕T1⊕T2; J=4→A1⊕E⊕T1⊕T2. Lattice operators are built from quark fields ψ(x) and gauge links U_μ(x) ∈ SU(3), with group-theoretic projection: O_Γ = Σ_{R∈O_h} χ_Γ(R) R[O_cont], where χ_Γ is the character of irrep Γ. The cubic lattice spacing a breaks rotational invariance; continuum limit restores SO(3) via a→0 with renormalization factors Z_Γ(aμ) matching lattice to continuum operators. | CONNECTION: The octahedral group O_h (order 48) is the full symmetry of the cube — a crystallographic point group. Its irreps (A1, A2, E, T1, T2) are the same branching rules found in crystal field theory. The ratio of lattice spacing to correlation len Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com