{
"schema_version": 1,
"kind": "ConceptView",
"producer": "concept-view-1",
"concept_id": "urn:uuid:82788b92-e7e2-458d-aa00-d14e5448427a",
"labels": {
"zh-CN": "反常",
"en": "moment-map anomaly"
},
"alternative_labels": [],
"scope_note": "",
"identity_status": "active",
"identity_revision": "a06f6575ff57e4b489ff6e52fad01c831dae344f2a744e16a1618a67c51a6556",
"occurrences": [
{
"concept_id": "urn:uuid:82788b92-e7e2-458d-aa00-d14e5448427a",
"book_id": "woit-qtgr",
"edition_id": "2025-10-20",
"lang": "zh-CN",
"route": "books/woit-qtgr/2025-10-20/zh/chapter-15/03-group-actions-on-m-and-the-moment-map",
"anchor": "first-47bbbd204887dc38bdee-zh",
"chapter": "15",
"section": "15.3",
"offset": 2191,
"range": [
9078,
9392
],
"source_revision": "93227314eb27987804b3a7a69011011c8c9bba7d67cbb387d7e32c38848439c9",
"source_category": "machine_draft",
"review_status": "machine-draft-not-reviewed",
"role": "occurrence",
"role_basis": {
"kind": "explicit-source-uuid-marker"
},
"label": "反常(moment-map anomaly)",
"context": {
"range": [
8979,
9459
],
"quote": "是从李代数 $\\mathfrak g$ 到 $M$ 上函数所成李代数的李代数同态。若能如此选择常数，就称该作用为哈密顿 $G$-作用。若无法作出这样的选择，则称 $G$ 在经典相空间上的作用存在“[反常(moment-map anomaly)](../../../../../concepts/symplectic-geometry/moment-map-anomaly)”。",
"quote_sha256": "60e061cf623d890cf3adba3ced2aba94a80d1d5e7415c5813b906e74d4de195c",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "books/woit-qtgr/2025-10-20/en/chapter-15/03-group-actions-on-m-and-the-moment-map",
"lang": "en",
"source_category": "machine_draft",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-3e99b0eb89ff9b970c83a838"
},
{
"concept_id": "urn:uuid:82788b92-e7e2-458d-aa00-d14e5448427a",
"book_id": "woit-qtgr",
"edition_id": "2025-10-20",
"lang": "zh-CN",
"route": "books/woit-qtgr/2025-10-20/zh/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"anchor": "source-25-5-moment-map-anomaly-title",
"chapter": "25",
"section": "25.5",
"offset": 150,
"range": [
6959,
7238
],
"source_revision": "78ad62caa1fc8b74672b7c08b1e8e56f54bb707db4ac5c89e145ab585c8bcb1b",
"source_category": "machine_draft",
"review_status": "machine-draft-not-reviewed",
"role": "occurrence",
"role_basis": {
"kind": "explicit-source-uuid-marker"
},
"label": "反常(moment-map anomaly)",
"context": {
"range": [
6941,
7303
],
"quote": "## 25.5 有限维中的正规序与[反常(moment-map anomaly)](../../../../../concepts/symplectic-geometry/moment-map-anomaly)",
"quote_sha256": "8e0227766eae87f6675a611163041ff5539bbf6dac71a297189d8e3a850d408c",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "books/woit-qtgr/2025-10-20/en/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"lang": "en",
"source_category": "machine_draft",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-6b7f6896fb65791483f06f2c"
},
{
"concept_id": "urn:uuid:82788b92-e7e2-458d-aa00-d14e5448427a",
"book_id": "woit-qtgr",
"edition_id": "2025-10-20",
"lang": "zh-CN",
"route": "books/woit-qtgr/2025-10-20/zh/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"anchor": "source-25-5-moment-map-anomaly-definition",
"chapter": "25",
"section": "25.5",
"offset": 2595,
"range": [
9404,
9683
],
"source_revision": "78ad62caa1fc8b74672b7c08b1e8e56f54bb707db4ac5c89e145ab585c8bcb1b",
"source_category": "machine_draft",
"review_status": "machine-draft-not-reviewed",
"role": "occurrence",
"role_basis": {
"kind": "explicit-source-uuid-marker"
},
"label": "反常(moment-map anomaly)",
"context": {
"range": [
9229,
9783
],
"quote": "正规序算符延拓到 $\\mathfrak{sp}(2d,\\mathbb R)$ 后，不再给出李代数同态；不过偏差仅是一个常数项。回顾[第15.3节](../chapter-15/03-group-actions-on-m-and-the-moment-map#section-15-3)，即使在经典层面，矩映射也只确定到一个加法常数；这可能造成一种“[反常(moment-map anomaly)](../../../../../concepts/symplectic-geometry/moment-map-anomaly)”：矩映射因常数项而不再是李代数同态。这里的潜在反常可以通过平移消除。",
"quote_sha256": "eaa478fc0e95cbabb8ebb5e7b90366db7aa55bcb138bb5658c35c5023a4275c5",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "books/woit-qtgr/2025-10-20/en/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"lang": "en",
"source_category": "machine_draft",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-fdf72f84e7460bf82075e5cd"
}
],
"registered_positions": [
{
"route": "books/woit-qtgr/2025-10-20/zh/chapter-15/03-group-actions-on-m-and-the-moment-map",
"lang": "zh-CN",
"section": "15.3",
"signal": "term-mark",
"label": "反常",
"english": "moment-map anomaly",
"offset": 2120
},
{
"route": "books/woit-qtgr/2025-10-20/zh/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"lang": "zh-CN",
"section": "25.5",
"signal": "term-mark",
"label": "反常",
"english": "moment-map anomaly",
"offset": 150
},
{
"route": "books/woit-qtgr/2025-10-20/zh/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"lang": "zh-CN",
"section": "25.5",
"signal": "term-mark",
"label": "反常",
"english": "moment-map anomaly",
"offset": 2439
}
],
"statements": [],
"resolved_references": [
{
"raw": "[第15.3节](../chapter-15/03-group-actions-on-m-and-the-moment-map#section-15-3)",
"href": "../chapter-15/03-group-actions-on-m-and-the-moment-map#section-15-3",
"range": [
9294,
9371
],
"relation": "references",
"target_route": "books/woit-qtgr/2025-10-20/zh/chapter-15/03-group-actions-on-m-and-the-moment-map",
"target_anchor": "section-15-3",
"resolved": true,
"reason": null,
"source_revision": "78ad62caa1fc8b74672b7c08b1e8e56f54bb707db4ac5c89e145ab585c8bcb1b",
"source_route": "books/woit-qtgr/2025-10-20/zh/chapter-25/07-normal-ordering-and-the-anomaly-in-finite-dimensions",
"occurrence_id": "occ-fdf72f84e7460bf82075e5cd"
}
],
"reading_order": [
"occ-3e99b0eb89ff9b970c83a838",
"occ-6b7f6896fb65791483f06f2c",
"occ-fdf72f84e7460bf82075e5cd"
],
"recorded_dependencies": [],
"reading_paths": [],
"coverage": {
"registered_positions": 3,
"located_occurrences": 3,
"whole_book_search_complete": false,
"registered_positions_truncated": false,
"independent_human_review_implied": false
},
"unresolved": [],
"base_revision": "a7613d3843785aef01b7fec15889053af52ebc547cf853f21284d01134b9f33d",
"optional_enrichments": []
}