Staggered Fermions Link Minimal Doubling to B4 Weyl Topology — E8 Intelligence Research

FINDING: Staggered lattice fermions realize minimally doubled chiral fermions with C, P, T symmetry, connecting Weyl semimetal topology to the B4 Weyl group root system. | MATH: The staggered fermion action yields two chiral doublers (minimal doubling) with dispersion \(E^2 = \sum_i \sin^2(k_i a)\); the B4 Cartan matrix \(A_{ij} = 2\delta_{ij} - \delta_{|i-j|,1}\) (with \(\det A = 1\) for B4) encodes the 4D hypercubic lattice's root system \(B_4\) (24 roots, \(|\alpha|^2 = 1\) or 2). Chiral symmetry \(\{\Gamma_5, D\} = 0\) is preserved via staggered \(\Gamma_5 = \gamma_5 \otimes \sigma_3\). | CONNECTION: The B4 root system's Weyl group order \(|W(B_4)| = 2^4 \cdot 4! = 384\) matches the hypercubic lattice's symmetry; the ratio of long to short roots is \(\sqrt{2}\) (≈1.414), and the Cartan matrix eigenvalues are \(2 - 2\cos(\pi m/5)\) for \(m=1..4\), giving ratios like \(0.382\) (for \(m=4\): \(2-2\cos(4\pi/5) = 2 - 2(-0.809) = 3.618\), whose reciprocal is 0.276 — but the golden ratio Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com