Lattice Gauge Theory: Non-Perturbative QCD via Monte Carlo on a Spacetime Grid — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Lattice gauge theory provides a discrete computational framework for quantum field theories, enabling non-perturbative QCD calculations via Monte Carlo methods on a spacetime grid. | MATH: Wilson action \( S_G = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{N} \text{Re Tr}\, U_{\mu\nu} \right) \), with \( \beta = 2N/g^2 \) for SU(N); link variables \( U_\mu(x) \in SU(3) \); lattice spacing \( a \) as UV regulator; continuum limit \( a \to 0 \) with renormalized coupling \( g(a) \); heavy-quark mass extraction via meson mass splittings \( M_{H_s} - M_{\eta_s} \) and one-loop perturbative matching. | CONNECTION: The lattice itself is a hypercubic grid — a discrete subgroup of the Euclidean translation group, breaking continuous rotational symmetry to the cubic point group \( O_h \) (order 48). This is a crystallographic symmetry (cubic system), directly analogous to space-group symmetries in crystals. The plaquette action is invariant under local gauge transformations \( U_\ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221511071
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