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.