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August 23, 2026Open Access

Symmetry Breaking, Topological Transitions, and Modified Wigner-Eckart Relations — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Theoretical analysis reveals modified Wigner-Eckart relations under symmetry breaking, highlighting exceptions to the Landau paradigm in topological transitions.

Key Points

  • To evaluate the limits of symmetry-breaking paradigms in phase transitions and determine how spontaneous symmetry breaking alters Wigner-Eckart selection rules.
  • Applied group-theoretic decomposition of group G into unbroken subgroup H to examine quantum selection rules.
  • Calculated corrections to the Wigner-Eckart theorem using Clebsch-Gordan coefficients in infinite systems.
  • Demonstrated that phase transitions do not universally require symmetry breaking, confirming topological transitions as key exceptions.
  • Derived modified Wigner-Eckart relations that connect broken symmetry states to crystallographic point groups, root systems, and fractional statistics.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a8aade47677a341144466c0https://doi.org/10.5281/zenodo.22022417
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  1. 1Phase Transitions Without Symmetry Breaking Challenge Landau Paradigm — E8 Intelligence Research2026
  2. 2Symmetry Breaking Corrections to Wigner-Eckart Relations in Infinite Systems — E8 Intelligence Research2026
  3. 3Beyond Landau: Symmetry Breaking and Wigner-Eckart Corrections in Infinite Systems — E8 Intelligence Research2026
  4. 4Symmetry Breaking Corrections to Wigner-Eckart Relations in Extended Systems — E8 Intelligence Research2026
  5. 5Phase Transitions Without Symmetry Breaking: Challenging Landau Paradigm — E8 Intelligence Research2026