Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

Andrew Stewart Caldin

doi:10.5281/zenodo.21897980

August 12, 2026Open Access

Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

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Key Points

Investigate the geometric and algebraic connection between massless 2D Dirac fermions in hexagonal graphene lattices and the crystallographic A2 root system.
Modeled 2D Dirac equations across defined hexagonal lattice vectors and reciprocal lattice vectors.
Evaluated Berry curvature localization at K and K' symmetry points alongside geometric lattice ratios.
Demonstrated that the 2D hexagonal lattice serves as a physical realization of the A2 root system corresponding to SU(3) symmetry.
Observed characteristic 60° and 120° angles and the √3 (≈ 1.732) scaling factor in lattice spacing and Dirac cone geometry, with Berry curvature concentrated at K and K' points.
Confirmed the absence of golden ratio or base-60 geometric structures within the analyzed lattice framework.

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Implication

Theoretical analysis reveals Dirac fermion dynamics align with A2 root system geometry in 2D hexagonal lattices, highlighting fundamental symmetry links between condensed matter and Lie algebras.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a7ec707b70b84ec8b91324f https://doi.org/10.5281/zenodo.21897980

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Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

Key Points

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Discussion

Cite This Study

Graphene's Dirac Fermions and A2 Root System Symmetry in Hexagonal Lattices — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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