{
  "abstract": "How can noncommuting quantum observables retain the geometry of a classical phase space? Motivated by Mumford's question on approximately macroscopically unique (AMU) states and the work of Lin and Wang, we study synthetic spectra of position--momentum and angular-momentum systems. Under the hypotheses of their AMU theorems, nonempty synthetic spectra yield AMU states. For sufficiently small $\\hbar$, the position--momentum spectrum fills the plane, while the angular-momentum spectrum contains any prescribed ball. The latter calculation leads to compact Lie groups: we prove that highest-weight coadjoint orbits lie in regional synthetic spectra under an explicit variance bound. Function-space representations of $SU(n)$, $SO(n)$, and $Sp(n)$ provide further examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04306",
  "author_total": 4,
  "authors": [
    {
      "name": "Junyang Liu"
    },
    {
      "name": "Hang Wang"
    },
    {
      "name": "Houjin Wang"
    },
    {
      "name": "Haoran Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f83jr9rrd50sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04306",
  "fulltext_url": null,
  "id": "f83jr9rrd50sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04306",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04306",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f83jr9rrd50sr.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04306",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04306"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups",
  "title_text": "Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/f83jr9rrd50sr",
  "venue": "arXiv",
  "versions": []
}