A Cl(6) Three-Flavor Lattice Symbol, Its Chiral Scaling Limit, and the Hilbert-Schmidt Convergence Rate
Year: 2026
Type: preprint
Abstract: We construct a five-parameter Hermitian Cl(6) three-flavor lattice symbol on a homogeneous chain with incommensurate on-site energies and show that its chiral scaling limit exists unconditionally and equals the three-flavor chiral CAR net over L^2(R) x C^3. The lattice states converge weak-* to the positive-frequency quasi-free vacuum(Buchholz-Verch scaling framework, Araki quasi-free machinery), and the convergence holds in bounded-region Hilbert-Schmidt topology with rate O(a^p): p=1 in the generic case (nonzero Hessian of the dispersion at the Fermi point), p=2 at the S_3-symmetric point (vanishing Hessian, cubic leading correction). The half-line inclusion is a strict half-sided modular inclusion with positive lightray translation generator. The lattice half-chain factor is type III_1 (verified via the spectral-interval condition), and the type is preserved under the scaling limit by Araki quasi-equivalence. Twenty-nine independent numerical checks across six scripts support the analytic results. The construction is 1+1 and dimension-preserving; no claim about (3+1) spacetime is made.
Author: Firestone, Todd
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170041208
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