{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:d5f9da17-e94f-479d-90f0-7732d12ee03a", "labels": { "zh-CN": "有限维自伴算符", "en": "finite-dimensional self-adjoint operator" }, "alternative_labels": [ { "lang": "en", "value": "self-adjoint" }, { "lang": "en", "value": "self-adjoint operator" }, { "lang": "zh-CN", "value": "自伴算符" } ], "scope_note": "§1.4 explicitly qualifies the construction to finite-dimensional state space; §4.5 uses the finite-dimensional adjoint.", "identity_status": "active", "identity_revision": "c4de69a2b42f87f31a17f2a55bad7791ac5a5e96db480c3ee2ef1bb5a80afb53", "occurrences": [ { "concept_id": "urn:uuid:d5f9da17-e94f-479d-90f0-7732d12ee03a", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-01/04-representations-and-quantum-mechanics", "anchor": "concept-1-self-adjoint-operator", "chapter": "1", "section": "1.4", "offset": 2028, "range": [ 10243, 10572 ], "source_revision": "651b93af49354643df29235b5d5a8624db703c2491d04f67cb8fa292c50899ca", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自伴算符(self-adjoint operator)", "context": { "range": [ 10135, 11000 ], "quote": "因此，至少在有限维态空间 $\\mathcal{H}$ 的情形下，由群 $G$ 在物理系统上的作用所诱导的 $G$ 在 $\\mathcal{H}$ 上的酉表示 $\\pi$，不仅给出酉矩阵 $\\pi(g)$，还给出相应的自伴算符(self-adjoint operator) $B$。李群作用因此为我们提供了一类[量子可观测量(quantum observable)](../../../../../concepts/quantum-mechanics/quantum-observable)；这些算符的自伴性恰好对应着态空间上表示的酉性。令人惊讶的是，在许多物理系统中，以这种方式得到的可观测量包括物理上最重要的那些。", "quote_sha256": "72645aa610b4896ed29c357432053c6b6367b0ab56d3baefb6fe2949f125f01e", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-01/04-representations-and-quantum-mechanics", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-080efdaf429ea940e8183647" }, { "concept_id": "urn:uuid:d5f9da17-e94f-479d-90f0-7732d12ee03a", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-04/05-adjoint-operators", "anchor": "concept-4-self-adjoint-operator", "chapter": "4", "section": "4.5", "offset": 1696, "range": [ 7892, 8184 ], "source_revision": "407e1079b0b6b24be173efe6c00066f6001dccb8a0c0caf1ab0376990bac1b24", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自伴算符(self-adjoint operator)", "context": { "range": [ 7847, 8613 ], "quote": "在实情形下，伴随算符的矩阵就是转置矩阵。若 $L^\\dagger=L$，则称 $L$ 为[自伴算符(self-adjoint operator)]；若 $L^\\dagger=-L$，则称 $L$ 为[斜伴随算符(skew-adjoint operator)]。", "quote_sha256": "99200e416040f55e870082ecdaf80d60ac345c75d83c121177e3ff36b134e913", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-04/05-adjoint-operators", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-66ded116bfb08befdb211d97" }, { "concept_id": "urn:uuid:d5f9da17-e94f-479d-90f0-7732d12ee03a", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-04/05-adjoint-operators", "anchor": "first-6c95bef6a9cf492f405a-en", "chapter": "4", "section": "4.5", "offset": 2168, "range": [ 7624, 7936 ], "source_revision": "cd9f99f91376f3deea8f9551c71a0c0de1b0b8de1d032daaa7bb5f1c3a28b7bf", "source_category": "original_transcription", "review_status": "ai-transcription-compared", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "self-adjoint", "context": { "range": [ 7459, 8275 ], "quote": "In the real case, the matrix of the adjoint is the transpose. 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