Renormalization Group Fixed Points in Lattice QCD and Conformal Gauge Theories — E8 Intelligence Research

FINDING: Renormalization group fixed points in lattice QCD and conformal gauge theories define scale-invariant limits where coupling constants become constant, enabling non-perturbative continuum definitions. | MATH: Fixed point condition: β(g*) = 0, where β(g) = μ dg/dμ; anomalous dimension γ_m = -d ln m / d ln μ at fixed point; critical exponents ν = 1/(d - θ) for correlation length; lattice spacing a → 0 at fixed point yields continuum limit. | CONNECTION: Fixed points correspond to self-similar (scale-invariant) states, analogous to geometric self-similarity ratios (e.g., 1.618 in golden spiral scaling). Lattice discretization imposes crystallographic symmetry (e.g., hypercubic lattice, root system A_3 for SU(3) QCD). Base-60 not directly present, but lattice actions often use rational approximations (e.g., Wilson action with coefficients 1, 0, ...). | DEPTH: 8 — Fixed points are central to renormalization group theory, linking quantum field theory to statistical mechanics and crit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com