Lattice Gauge Theory: Wilson Action and Monte Carlo Computation of Yang–Mills — E8 Intelligence Research

FINDING: Lattice gauge theory discretises continuous gauge fields onto a hypercubic spacetime lattice, making the Yang–Mills path integral finite-dimensional and computable via Monte Carlo methods. | MATH: Wilson action S = β Σ_□ (1 − (1/N) Re Tr U_□), where U_□ = U_μ(x) U_ν(x+μ̂) U_μ†(x+ν̂) U_ν†(x) is the plaquette (elementary square loop), β = 2N/g² for SU(N). Continuum limit: a → 0, β → ∞. Gauge link U_μ(x) = exp(ig a A_μ(x)) ∈ SU(N). | CONNECTION: The lattice is a Z⁴ hypercubic Bravais lattice — a crystallographic root system of type B₄/C₄. Plaquettes are the 2-cells of the cubical CW-complex; the lattice gauge field is a 1-cochain with values in the gauge group, and the field strength is its coboundary (curvature 2-form). This is discrete differential geometry: the lattice realises the de Rham complex combinatorially. | DEPTH: 7 --- FINDING: Heavy-quark masses are extracted from lattice QCD by matching meson mass correlators computed on the lattice to continuum perturbation theo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com