Lattice Gauge Theory: Discretizing QCD for Non-Perturbative Calculations — E8 Intelligence Research

Abstract

FINDING: Gauge theory on a lattice discretizes continuous symmetries into discrete group elements, enabling non-perturbative QCD calculations via path integrals over finite grid points. | MATH: Key structure: SU(3) gauge group for QCD; lattice spacing \(a\) regularizes UV divergences; Wilson action \(S = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{3} \text{Re Tr}(U_\square)\right)\) with \(\beta = 6/g^2\); heavy-quark mass extraction uses one-loop perturbative matching to continuum. | CONNECTION: Lattice discretization inherently links to crystallographic symmetry — the hypercubic lattice is a Bravais lattice with point group \(O_h\) (octahedral symmetry), a finite subgroup of the continuous rotation group. The lattice spacing ratio \(a\) sets a scale; no direct golden ratio or base-60 appears in these findings. | DEPTH: 6 — Lattice gauge theory is a profound computational tool for non-perturbative QCD, but the specific findings here (heavy-quark masses from Fermilab method) are Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com