{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:7a317edb-3bbe-49f4-b908-1db5e9edf4bc",
  "labels": {
    "zh-CN": "辛流形",
    "en": "symplectic manifold"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "799f2a55b8231e597941fdf7d4455405d1ff1c511bb6e2a8a50741371fcab192",
  "occurrences": [
    {
      "concept_id": "urn:uuid:7a317edb-3bbe-49f4-b908-1db5e9edf4bc",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-16/05-classical-mechanics",
      "anchor": "first-658e3cca18d5c3d420ca-zh",
      "chapter": "16",
      "section": "16.5",
      "offset": 25857,
      "range": [
        33637,
        33880
      ],
      "source_revision": "aac6045c8f792acfb5c9989193835b417610f4c945fe5f70074b9b0c3fb0e939",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "辛流形(symplectic manifold)",
      "context": {
        "range": [
          33141,
          33881
        ],
        "quote": "若存在非退化 2-形式，则流形 $M$ 的维数必为偶数 $m = 2 n$，因为 $\\det A \\det \\mathbf { A } ^ { T } = \\operatorname* { d e t } ( - \\mathbf { A } ) = ( - 1 ) ^ { m } \\det A$。$2n$ 维流形 $M$ 上的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:128dd2b3-9341-4ec8-80d7-756b3c868174\" data-concept-route=\"/concept-identities#concept-128dd2b3-9341-4ec8-80d7-756b3c868174\" id=\"first-d0cb31504300ef340ba8-zh\">辛结构(symplectic structure)</u> 是一个闭的可微 2-形式 $\\Omega$，且处处非退化。回忆闭的意味着处处有 $\\mathrm { d } \\Omega = 0$。带有辛结构的偶数维流形 $M$ 称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:7a317edb-3bbe-49f4-b908-1db5e9edf4bc\" data-concept-route=\"/concept-identities#concept-7a317edb-3bbe-49f4-b908-1db5e9edf4bc\" id=\"first-658e3cca18d5c3d420ca-zh\">辛流形(symplectic manifold)</u>。",
        "quote_sha256": "aad8996b1bbd9f0b5fa2f0ae4a66003973125fcb88e6864c53e8fca3175be729",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-16/05-classical-mechanics",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-0cfa6ad7767c8a664f54a1b0"
    },
    {
      "concept_id": "urn:uuid:7a317edb-3bbe-49f4-b908-1db5e9edf4bc",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "en",
      "route": "en/chapter-16/05-classical-mechanics",
      "anchor": "first-658e3cca18d5c3d420ca-en",
      "chapter": "16",
      "section": "16.5",
      "offset": 34575,
      "range": [
        41884,
        42122
      ],
      "source_revision": "6ba31cc0cea910b2bb1780c9e846e4e265229202d450afd615e6b7053ad533bb",
      "source_category": "original_transcription",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "symplectic manifold",
      "context": {
        "range": [
          41167,
          42123
        ],
        "quote": "The manifold $M$ must necessarily be of even dimension $m = 2 n$ if there exists a non degenerate 2-form, since $\\det A \\det \\mathbf { A } ^ { T } = \\operatorname* { d e t } ( - \\mathbf { A } ) = ( - 1 ) ^ { m } \\det A$. A <u class=\"concept-term\" data-concept-identity=\"urn:uuid:128dd2b3-9341-4ec8-80d7-756b3c868174\" data-concept-route=\"/concept-identities#concept-128dd2b3-9341-4ec8-80d7-756b3c868174\" id=\"first-d0cb31504300ef340ba8-en\">symplectic structure</u> on a $2n$-dimensional manifold $M$ is a closed differentiable 2-form $\\Omega$ that is everywhere non-degenerate. Recall that closed means that $\\mathrm { d } \\Omega = 0$ everywhere. An even-dimensiona manifold $M$ with a symplectic structure is called a <u class=\"concept-term\" data-concept-identity=\"urn:uuid:7a317edb-3bbe-49f4-b908-1db5e9edf4bc\" data-concept-route=\"/concept-identities#concept-7a317edb-3bbe-49f4-b908-1db5e9edf4bc\" id=\"first-658e3cca18d5c3d420ca-en\">symplectic manifold</u>.",
        "quote_sha256": "33ea243a4afa371118f12c77f3efceba98931700f9261fa65abe0803274730ee",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "zh/chapter-16/05-classical-mechanics",
          "lang": "zh-CN",
          "source_category": "translation",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-2e6e1602315044a2b87a4220"
    }
  ],
  "registered_positions": [
    {
      "route": "en/chapter-16/05-classical-mechanics",
      "lang": "en",
      "section": "16.5",
      "signal": "term-mark",
      "label": "symplectic manifold",
      "english": "symplectic manifold",
      "offset": 32856
    },
    {
      "route": "zh/chapter-16/05-classical-mechanics",
      "lang": "zh-CN",
      "section": "16.5",
      "signal": "term-mark",
      "label": "辛流形",
      "english": "symplectic manifold",
      "offset": 24138
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-0cfa6ad7767c8a664f54a1b0",
    "occ-2e6e1602315044a2b87a4220"
  ],
  "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": "2b441f831ec52bcd19876733f88ca741d5aad41e5566a11ff020a8a6b089b0af",
  "optional_enrichments": []
}