Lattice Gauge Theory: Discretized Quantum Fields and Thermalization Dynamics — E8 Intelligence Research

FINDING: Lattice gauge theory (LatticeQCD.jl, 2+1D gauge theories, disorder-free localization, thermalization) computes non-perturbative quantum field dynamics via discretized spacetime grids, with recent focus on quantum simulation of gauge fields. | MATH: Lattice discretization replaces continuous gauge group SU(3) (QCD) with finite-dimensional link variables \(U_\mu(x) \in SU(3)\); Wilson action \(S_W = \beta \sum_{\text{plaquettes}} \left(1 - \frac{1}{N} \text{Re Tr}\, U_{\square}\right)\), \(\beta = 2N/g^2\); for 2+1D gauge theory, coupling \(g^2\) has mass dimension 1, dimensionless ratio \(g^2 a\) (lattice spacing \(a\)); disorder-free localization arises from Hilbert-space fragmentation — conserved quantities from Gauss's law \(\nabla \cdot E = \rho\) on lattice; thermalization studied via entanglement entropy \(S = -\text{Tr}(\rho \log \rho)\) and spectral form factor \(g(\tau) = |Z(\beta + i\tau)/Z(\beta)|^2\). | CONNECTION: Lattice gauge theory is inherently a **root-system Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com