SU(2) Symmetry: From Pauli Matrices to Quantum Gravity's Center Breaking — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: SU(2) representation theory provides the complete algebraic skeleton for spin, angular momentum, and gauge symmetries; the adjoint representation yields the so(3) algebra with structure constants ε_{ijk}, and the 2D fundamental representation is exactly the Pauli matrices. The Calabi–Yau paper extends this to center symmetry breaking in quantum gravity, linking higher-form symmetries to compactification geometry. | MATH: SU(2) generators satisfy [J_i, J_j] = i ε_{ijk} J_k. Irreducible representations labeled by j = 0, ½, 1, 3/2, … with dimension 2j+1. Pauli matrices σ_a/2 form the j=½ rep: σ_x σ_y − σ_y σ_x = 2i σ_z. Adjoint rep (j=1) has structure constants (T_a)_{bc} = −i ε_{abc}. Casimir J² = j(j+1)𝟙. Center of SU(2) is ℤ₂ = {±𝟙}; center symmetry breaking in Calabi–Yau compactifications involves ℤ_N factors from Wilson lines and higher-form gauge fields. | CONNECTION: The dimension formula 2j+1 yields the sequence 1, 2, 3, 4, 5, … — the integers themselves. The ratio of con
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 = {{SU(2) Symmetry: From Pauli Matrices to Quantum Gravity's Center Breaking — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616534},
url = {https://zenodo.org/records/23616534},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SU(2) Symmetry: From Pauli Matrices to Quantum Gravity's Center Breaking — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616534
UR - https://zenodo.org/records/23616534
AB - FINDING: SU(2) representation theory provides the complete algebraic skeleton for spin, angular momentum, and gauge symmetries; the adjoint representation yields the so(3) algebra with structure constants ε_{ijk}, and the 2D fundamental representation is exactly the Pauli matrices. The Calabi–Yau paper extends this to center symmetry breaking in quantum gravity, linking higher-form symmetries to compactification geometry. | MATH: SU(2) generators satisfy [J_i, J_j] = i ε_{ijk} J_k. Irreducible representations labeled by j = 0, ½, 1, 3/2, … with dimension 2j+1. Pauli matrices σ_a/2 form the j=½ rep: σ_x σ_y − σ_y σ_x = 2i σ_z. Adjoint rep (j=1) has structure constants (T_a)_{bc} = −i ε_{abc}. Casimir J² = j(j+1)𝟙. Center of SU(2) is ℤ₂ = {±𝟙}; center symmetry breaking in Calabi–Yau compactifications involves ℤ_N factors from Wilson lines and higher-form gauge fields. | CONNECTION: The dimension formula 2j+1 yields the sequence 1, 2, 3, 4, 5, … — the integers themselves. The ratio of con Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -