{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:4c74fea1-7d81-4015-bdee-4561d67bcd4d",
  "labels": {
    "zh-CN": "规范群",
    "en": "Gauge group"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "d8c63c75629ea6ff0fe835c8e12244a43e437d475f8aaec4cafe4bd9a6f31427",
  "occurrences": [
    {
      "concept_id": "urn:uuid:4c74fea1-7d81-4015-bdee-4561d67bcd4d",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-45/01-u-1-gauge-symmetry",
      "anchor": "first-93f4e0d9093d61909885-zh",
      "chapter": "45",
      "section": "45.1",
      "offset": 238,
      "range": [
        6799,
        7023
      ],
      "source_revision": "e76063abd34928456edd1214b6a1b939b5a221a6a8c3ed8067b71c6737e9e533",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "definition",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-45/01-u-1-gauge-symmetry",
          "lang": "zh-CN",
          "section": "45.1",
          "signal": "named-definition",
          "label": "规范群",
          "english": "",
          "offset": 168
        }
      },
      "label": "> [!definition] 定义（规范群）",
      "context": {
        "range": [
          6799,
          7023
        ],
        "quote": "\n\n> [!definition] 定义（规范群）\n> 定义在 $M ^ { 4 }$ 上、取值于单位圆 $U ( 1 )$ 的函数构成的群 $\\mathcal { G }$，其群法则由逐点乘法给出\n>\n> $$\n> e ^ {i e \\varphi_ {1} (x)} \\cdot e ^ {i e \\varphi_ {2} (x)} = e ^ {i e (\\varphi_ {1} (x) + \\varphi_ {2} (x))}\n> $$\n",
        "quote_sha256": "cc29ca090c28031061391e9dc160a85a92ab053bfddf43f5e0607e12eb069d8b",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-45/01-u-1-gauge-symmetry",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-46de8444ab7df583ddc70830"
    },
    {
      "concept_id": "urn:uuid:4c74fea1-7d81-4015-bdee-4561d67bcd4d",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-45/01-u-1-gauge-symmetry",
      "anchor": "first-3bfc8e9d948f62d50be7-en",
      "chapter": "45",
      "section": "45.1",
      "offset": 803,
      "range": [
        6523,
        6837
      ],
      "source_revision": "571e8d595fef9205d90a7809922985c70c78661083075ba1c498336e3a4adcd0",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-45/01-u-1-gauge-symmetry",
          "lang": "en",
          "section": "45.1",
          "signal": "named-theorem",
          "label": "Gauge group",
          "english": "Gauge group",
          "offset": 733
        }
      },
      "label": "> [!theorem] Definition (Gauge group)",
      "context": {
        "range": [
          6523,
          6837
        ],
        "quote": "\n\n> [!theorem] Definition (Gauge group)\n> The group $\\mathcal { G }$ of functions on $M ^ { 4 }$ with values in the unit circle $U ( 1 )$ , with group law given by point-wise multiplication\n>\n> $$\n> e ^ {i e \\varphi_ {1} (x)} \\cdot e ^ {i e \\varphi_ {2} (x)} = e ^ {i e (\\varphi_ {1} (x) + \\varphi_ {2} (x))}\n> $$\n",
        "quote_sha256": "1ca7fbe94aa5e2de59bfa8f959ea49ceed307226560d241d8189d2020772bcc8",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-45/01-u-1-gauge-symmetry",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-2327511792bd318bf36583bc"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-45/01-u-1-gauge-symmetry",
      "lang": "en",
      "section": "45.1",
      "signal": "named-theorem",
      "label": "Gauge group",
      "english": "Gauge group",
      "offset": 733
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-45/01-u-1-gauge-symmetry",
      "lang": "zh-CN",
      "section": "45.1",
      "signal": "named-definition",
      "label": "规范群",
      "english": "",
      "offset": 168
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-46de8444ab7df583ddc70830",
    "occ-2327511792bd318bf36583bc"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 2,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "1d759cf08215b4448ca5d5973b6746f7b5020f558b02c44f3a112cad33ad5b13",
  "optional_enrichments": []
}
