{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:e8ca6ba1-6ef2-4a3a-a299-bd7c3a6498b5",
  "labels": {
    "zh-CN": "相对论复结构",
    "en": "Relativistic complex structure"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "81b350c47550574957d9dab3ff553f385c284eef10d072e97ee23b1342a851e9",
  "occurrences": [
    {
      "concept_id": "urn:uuid:e8ca6ba1-6ef2-4a3a-a299-bd7c3a6498b5",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-43/02-the-symplectic-and-complex-structures-on-m",
      "anchor": "first-74d2487b15a60777c141-zh",
      "chapter": "43",
      "section": "43.2",
      "offset": 3205,
      "range": [
        10527,
        10955
      ],
      "source_revision": "9173982298ff1f39432f486f3650090bd303d8c6c4384f2b39e28d58069776ce",
      "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-43/02-the-symplectic-and-complex-structures-on-m",
          "lang": "zh-CN",
          "section": "43.2",
          "signal": "named-definition",
          "label": "相对论复结构",
          "english": "",
          "offset": 3135
        }
      },
      "label": "> [!definition] 定义（相对论复结构）",
      "context": {
        "range": [
          10527,
          10955
        ],
        "quote": "\n\n> [!definition] 定义（相对论复结构）\n> 实解空间 $\\mathcal { M }$ 上的相对论复结构由算符 $J_r$ 给出。将它延拓到 $\\mathcal { M }\\otimes\\mathbf{C}$ 后，它在 $\\alpha(\\mathbf{p})$ 上的作用为 $+i$，在 $\\overline{\\alpha}(\\mathbf{p})$ 上的作用为 $-i$。\n>\n> 于是 $A(\\mathbf{p})$ 构成 $\\mathcal{M}^+_{J_r}$ 的连续基，$\\overline{A}(\\mathbf{p})$ 构成 $\\mathcal{M}^-_{J_r}$ 的连续基，并且\n>\n> $$\n> \\mathcal {M} \\otimes \\mathbf {C} = \\mathcal {M} _ {J _ {r}} ^ {+} \\oplus \\mathcal {M} _ {J _ {r}} ^ {-}\n> $$\n",
        "quote_sha256": "157edbecb4cab685488ed0baff7e79192a89c8384cc1ff0d0c7dbd69b351b305",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-43/02-the-symplectic-and-complex-structures-on-m",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-02dd37a235671de0748b3f98"
    },
    {
      "concept_id": "urn:uuid:e8ca6ba1-6ef2-4a3a-a299-bd7c3a6498b5",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-43/02-the-symplectic-and-complex-structures-on-m",
      "anchor": "first-643e72c709a21d83d6b7-en",
      "chapter": "43",
      "section": "43.2",
      "offset": 6215,
      "range": [
        12694,
        12973
      ],
      "source_revision": "8e1f38aa81add0ec646025f9e52d61269aeca23409f0d044749f324c04abba9a",
      "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-43/02-the-symplectic-and-complex-structures-on-m",
          "lang": "en",
          "section": "43.2",
          "signal": "named-theorem",
          "label": "Relativistic complex structure",
          "english": "Relativistic complex structure",
          "offset": 6145
        }
      },
      "label": "> [!theorem] Definition (Relativistic complex structure)",
      "context": {
        "range": [
          12694,
          12973
        ],
        "quote": "\n\n> [!theorem] Definition (Relativistic complex structure)\n> The relativistic complex structure on the real solution space $M$ is the operator $J_r$ that, when extended to $M\\otimes\\mathbf{C}$, acts by $+i$ on $\\alpha(\\mathbf{p})$ and by $-i$ on $\\overline{\\alpha}(\\mathbf{p})$.\n",
        "quote_sha256": "143b837a8fd78698dfd2ceb560b639a48168835cf710c0a72fe232fe01ba5f63",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-43/02-the-symplectic-and-complex-structures-on-m",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-dd34a08b0847e88c226b03cf"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-43/02-the-symplectic-and-complex-structures-on-m",
      "lang": "en",
      "section": "43.2",
      "signal": "named-theorem",
      "label": "Relativistic complex structure",
      "english": "Relativistic complex structure",
      "offset": 6145
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-43/02-the-symplectic-and-complex-structures-on-m",
      "lang": "zh-CN",
      "section": "43.2",
      "signal": "named-definition",
      "label": "相对论复结构",
      "english": "",
      "offset": 3135
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-02dd37a235671de0748b3f98",
    "occ-dd34a08b0847e88c226b03cf"
  ],
  "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": "69e8986f05021db5fef68c816b6f2a7c81cada9701e13b6546c071b6084c3448",
  "optional_enrichments": []
}
