Lattice Gauge Theory: Non‑Perturbative Regularisation and Monte‑Carlo Hadron Spectrum Extraction — E8 Intelligence Research

FINDING: Lattice gauge theory provides a non‑perturbative regularisation of quantum gauge fields by discretising space‑time on a hypercubic (or more general) lattice, enabling Monte‑Carlo evaluation of path integrals and extraction of hadron spectra (e.g. heavy‑quark masses). | MATH: Euclidean action \(S_E = \sum_{x,\mu<\nu}\frac{1}{g^2}\,\text{Re}\,\text{Tr}\,[\mathbf{1}-U_{\mu\nu}(x)]\); link variable \(U_\mu(x)=\exp\big[i a g A_\mu(x)\big]\); Wilson fermion term \(S_F = \sum_{x,y}\bar\psi(x)D_{W}(x,y)\psi(y)\) with \(D_W = m_0 + \frac12\sum_\mu\big[\gamma_\mu(\nabla_\mu+\nabla^*_\mu)-a\nabla^*_\mu\nabla_\mu\big]\); heavy‑quark mass from Fermilab method \(M_H = Z_m\,m_0 + \delta M\). | CONNECTION: The underlying hypercubic lattice is a 4‑dimensional Bravais lattice with point‑group symmetry \(O_h\) (cubic crystallographic group). Its reciprocal lattice yields momentum space discretisation with spacing \(2\pi/a\); the symmetry group contains the root system \(B_4\) (or \(D_4\)) whose Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com