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March 27, 2026Open Access

FCC Uniqueness Among All Bravais Lattices and the Continuum Field Theory Limit of the SU(2) Neighbourhood Operators

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Authors

BHBruce Hunter

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Overview

This analysis demonstrates the uniqueness of the FCC lattice and its continuum limit in quantum field theory, suggesting new insights into Bravais lattices.

Key Points

  • The aim is to resolve the uniqueness of the FCC lattice among Bravais lattices and explore the continuum limit of neighbourhood operators.
  • Analyzed the classification of Bravais lattices based on Clifford grades.
  • Proved that FCC is the unique lattice meeting specific conditions using Theorem 3.1.
  • Showed convergence of FCC neighbourhood operators to the Clifford-algebra Dirac derivative as lattice spacing approaches zero.
  • FCC lattice is confirmed as the unique Bravais lattice satisfying three critical conditions.
  • Neighbouhood operators converge to the Dirac derivative with O(a²) corrections verified numerically.
  • The FCC lattice action yields the standard kinetic term of the SU(2) sigma model.

Cite This Study

Bruce Hunter (2026) studied this question.

synapsesocial.com/papers/69c61ff615a0a509bde18526https://doi.org/10.5281/zenodo.19212294
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  4. 4Spontaneous FCC Lattice Formation from Non-Local Scalar Field Theory: A Numerical Demonstration of the Non-Circular Derivation of Newton's G2026
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