D4 Symmetry in Square Lattice QCD and Pedagogical Resources — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results are primarily pedagogical videos and one lattice QCD paper; no direct new result on Dedekind eta modular symmetry order 4 or C4 partition is presented. The mathematical core is the crystallographic point group D4 (order 8) and its action on the square lattice, plus a lattice QCD mass calculation.
MATH: - Square lattice point group: D4 (dihedral of order 8), generated by 90° rotation r and reflection s, with relations r4 = s2 = (rs)2 = e. - Crystallographic restriction: only rotations of order 1,2,3,4,6 are allowed in 2D lattices — order 4 is maximal for square symmetry. - Dedekind eta function: η(τ) = q1/24 ∏n=1∞ (1−qn), q = e2π i τ. Modular transformations of order 4 correspond to τ ↦ (aτ+b)/(cτ+d) with a & b c & d ∈ SL(2,ℤ) and specific congruence conditions (e.g., Γ(4) or Γ0(4)).
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026symmetry,
title = {{D4 Symmetry in Square Lattice QCD and Pedagogical Resources — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23410094},
url = {https://zenodo.org/records/23410094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - D4 Symmetry in Square Lattice QCD and Pedagogical Resources — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23410094
UR - https://zenodo.org/records/23410094
AB - FINDING: The search results are primarily pedagogical videos and one lattice QCD paper; no direct new result on Dedekind eta modular symmetry order 4 or C4 partition is presented. The mathematical core is the crystallographic point group D4 (order 8) and its action on the square lattice, plus a lattice QCD mass calculation. MATH: - Square lattice point group: D4 (dihedral of order 8), generated by 90° rotation r and reflection s, with relations r^4 = s^2 = (rs)^2 = e. - Crystallographic restriction: only rotations of order 1,2,3,4,6 are allowed in 2D lattices — order 4 is maximal for square symmetry. - Dedekind eta function: η(τ) = q^1/24 ∏_n=1^∞ (1−q^n), q = e^2π i τ. Modular transformations of order 4 correspond to τ ↦ (aτ+b)/(cτ+d) with a & b c & d ∈ SL(2,ℤ) and specific congruence conditions (e.g., Γ(4) or Γ_0(4)). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -