Z₂⁴ Grading and B₄ Roots: Topological Invariant of Staggered Fermion Doubling — E8 Intelligence Research

Q: What does this research mean for the field?

Staggered fermion doubling is governed by a Z₂⁴ grading that maps to the B₄ root system, yielding a topological invariant tied to the 4D hypercubic lattice's Clifford algebra structure. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22470732

September 6, 2026Open Access

Z₂⁴ Grading and B₄ Roots: Topological Invariant of Staggered Fermion Doubling — E8 Intelligence Research

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Key Points

To establish the mathematical and topological structure underlying the 16-fold fermion doubling in staggered lattice field theory.
Analyzed the staggered fermion Dirac operator D_stag = Σ_μ γ_μ ⊗ ∇_μ on a 4D hypercubic lattice.
Mapped the Z₂⁴ lattice site grading ε_μ = (-1)^{x_μ} to reflection operators in the B₄ Weyl group of order 384.
Computed topological invariants via the second Chern number and the S⁴ → S⁴ winding number.
Staggered fermion doubling displays a 2⁴ = 16-fold multiplicity governed by a Z₂⁴ grading isomorphic to the commuting reflections of the B₄ Weyl group.
The topological invariant connects to the second Chern number Ch₂ = (1/32π²)∫Tr(F∧F) and evaluates directly to the winding number ν over the 4-sphere map.
The sign structure of the 24 roots of B₄ precisely corresponds to the Z₂⁴ lattice grading.

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Implication

Mathematical study reveals staggered fermion doubling maps to the B4 root system, indicating a topological invariant tied to lattice Clifford algebra.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9fd76758e84d0ff5b46077 https://doi.org/10.5281/zenodo.22470732

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Z₂⁴ Grading and B₄ Roots: Topological Invariant of Staggered Fermion Doubling — E8 Intelligence Research

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Z₂⁴ Grading and B₄ Roots: Topological Invariant of Staggered Fermion Doubling — E8 Intelligence Research

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Cite This Study

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