A Cl(6) Three-Flavor Lattice Symbol, Its Chiral Scaling Limit, and the Hilbert-Schmidt Convergence Rate
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.
Authors
- Todd Firestone (ORCID: https://orcid.org/0009-0006-3133-8292)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-07-22
- DOI
- https://doi.org/10.5281/zenodo.21495723
- Primary Topic
- Quantum Mechanics and Non-Hermitian Physics
- Type
- preprint