{
  "abstract": "FINDING: Spontaneous symmetry breaking (SSB) modifies Wigner–Eckart (WE) relations in infinite systems via volume-scaled corrections, not just perturbative shifts. | MATH: The WE theorem factorizes matrix elements as ⟨α′j′m′|T^(k)_q|αjm⟩ = ⟨jk;mq|j′m′⟩ · (reduced element)/√(2j′+1). The arXiv result (2007.03539) proves that when G is spontaneously broken, corrections to these relations scale as **1/√V** (volume V of the system), arising from Goldstone-mode contributions. Specifically, the correction to the reduced matrix element is proportional to ⟨0|φ_G|0⟩/√V, where φ_G is the Goldstone field, and the leading correction to the WE ratio is **O(V^{-1/2})**, vanishing in the thermodynamic limit but finite for finite systems. | CONNECTION: The 1/√V scaling is the square root of the inverse volume — echoing the ratio **0.7071** (√1/2) if normalized to a unit cell, but more fundamentally it ties to **spherical symmetry breaking down to a subgroup H ⊂ G**, whose coset space G/H has dimension\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh2ha0kdfh3e4.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490794",
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  "id": "bh2ha0kdfh3e4",
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  "landing_url": "https://zenodo.org/records/23490794",
  "language": "eng",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh2ha0kdfh3e4.ris",
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    {
      "first_seen": "2026-11-03T12:21:25Z",
      "native_id": "23490794",
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  "title": "Spontaneous Symmetry Breaking Alters Wigner–Eckart Relations via Volume-Scaled Goldstone Corrections — E8 Intelligence Research",
  "title_text": "Spontaneous Symmetry Breaking Alters Wigner–Eckart Relations via Volume-Scaled Goldstone Corrections — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:25Z",
  "url": "https://research.draconitic.com/paper/bh2ha0kdfh3e4",
  "venue": "Zenodo",
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