Lattice Gauge Theory via Wilson Action for Non-Perturbative QCD — E8 Intelligence Research

Abstract

FINDING: Gauge theory lattice computation (LatticeQCD.jl, lattice gauge theory) provides a discretized path-integral framework for non-perturbative QCD and topological field theories, with gauge symmetry encoded via link variables on a hypercubic lattice. | MATH: Wilson action \( S_G = \beta \sum_{\square} \left(1 - \frac{1}{N} \text{Re Tr}\, U_\square \right) \), \(\beta = 2N/g^2\); link variables \( U_\mu(n) \in SU(N) \); plaquette \( U_\square = U_\mu(n)U_\nu(n+\hat\mu)U_\mu^\dagger(n+\hat\nu)U_\nu^\dagger(n) \); continuum limit via \( a \to 0 \) with renormalization group flow \( g^2(a) \sim 1/\ln(1/a\Lambda) \). | CONNECTION: The lattice is a **crystallographic hypercubic lattice** (root system \( A_1^{\otimes d} \), \( d=4 \)), whose symmetry group is the hyperoctahedral group \( B_4 \) (order 384) — a finite Weyl group. The plaquette structure encodes **holonomy** (curvature) as a discrete parallel transport, directly analogous to the **golden-ratio-modulated** phase factors in Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com