Lattice Gauge Theory: Non-Perturbative QCD, Confinement, and Heavy-Quark Mass Extraction — E8 Intelligence Research

Abstract

FINDING: Lattice gauge theory discretizes continuous gauge fields onto a spacetime lattice for non-perturbative QCD computation, with confinement emerging from Wilson loop area-law behavior. | MATH: Wilson action: \( S = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{N} \text{Re Tr}[U_\square]\right) \), where \(\beta = 2N/g^2\) for SU(N). Confinement criterion: \(\langle W(C) \rangle \sim e^{-\sigma A}\) (area law), with string tension \(\sigma\). Heavy-quark mass extraction uses lattice perturbation theory: \( m_Q = m_{\text{lattice}} + \delta m \) from one-loop matching. | CONNECTION: Lattice discretization inherently involves crystallographic symmetry (hypercubic lattice in 4D, root system \(B_4\)). The plaquette action is a discrete curvature, analogous to parallel transport around a minimal square. No direct golden ratio or base-60 link; however, the lattice spacing \(a\) sets a scale, and continuum limit \(a \to 0\) recovers continuous gauge symmetry. | DEPTH: 7 — Foundationa Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com