{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:c4df2f3d-e41b-4bde-949e-8989739a863d", "labels": { "zh-CN": "de Rham微分", "en": "de Rham differential" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "854a940c15a6a0387725d13428f257fb460381b3c1ff7e7f7abc74f7c131a385", "occurrences": [ { "concept_id": "urn:uuid:c4df2f3d-e41b-4bde-949e-8989739a863d", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "anchor": "first-f2d1370f98e339cb27f5-zh", "chapter": "33", "section": "33.3", "offset": 584, "range": [ 7609, 7936 ], "source_revision": "d2db4e8eeeedf2be314f069d7d5856b6da37ac21f50b9b512b5a275505aeaa9d", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "de Rham微分(de Rham differential)", "context": { "range": [ 7372, 8458 ], "quote": "这是 $\\mathbb R^d$ 上复值函数空间与 $\\mathbb C^d$ 上反交换函数空间的张量积，分别受Weyl代数 $\\operatorname{Weyl}(2d,\\mathbb C)$ 和Clifford代数 $\\operatorname{Cliff}(2d,\\mathbb C)$ 作用。$Q_+,Q_-$ 互为伴随，且平方均为零。数学中，这个空间就是复值微分形式空间 $\\Omega^*(\\mathbb R^d)$；次数从 $0$（函数）到 $d$。其上的[de Rham微分(de Rham differential)](../../../../../concepts/differential-geometry/de-rham-differential) $d$ 满足 $d^2=0$。利用欧氏内积和积分，可在微分形式上定义厄米内积；$d$ 的伴随 $\\delta$ 同样平方为零。微分形式上的[拉普拉斯算符(Laplacian operator)](../../../../../concepts/differential-geometry/hodge-laplacian)为", "quote_sha256": "62e580a7be5088999c19ae82f917b92d059672d2fc69b07605d1d73e6cca021a", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-d8c705dca47a1b693e25bd86" }, { "concept_id": "urn:uuid:c4df2f3d-e41b-4bde-949e-8989739a863d", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "anchor": "first-f2d1370f98e339cb27f5-en", "chapter": "33", "section": "33.3", "offset": 917, "range": [ 7098, 7414 ], "source_revision": "d16cea66f70ed8fd0154df7f4315fd2ebcae08d5bc7b9bd3377be04a578ab7af", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "de Rham differential", "context": { "range": [ 6670, 8045 ], "quote": "This is the tensor product of complex-valued functions on $\\mathbb R^d$, acted on by $\\operatorname{Weyl}(2d,\\mathbb C)$, and anticommuting functions on $\\mathbb C^d$, acted on by $\\operatorname{Cliff}(2d,\\mathbb C)$. The mutually adjoint operators $Q_+,Q_-$ square to zero. Mathematicians recognize this space as the complex differential forms $\\Omega^*(\\mathbb R^d)$, where the degree ranges from $0$ (functions) to $d$. The [de Rham differential](../../../../../concepts/differential-geometry/de-rham-differential) $d$ squares to zero. The Euclidean inner product induces a Hermitian inner product on forms by integration; the adjoint $\\delta$ of $d$ also squares to zero. The [Laplacian operator on differential forms](../../../../../concepts/differential-geometry/hodge-laplacian) is", "quote_sha256": "ab2441987034e2145ed77c983f4e80738dfd73a90b02c7370240b33e783630e6", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-c3221aeb58474ee0a8edfdd2" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "lang": "en", "section": "33.3", "signal": "term-mark", "label": "de Rham differential", "english": "de Rham differential", "offset": 917 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-33/03-supersymmetric-quantum-mechanics-and-diferential-forms", "lang": "zh-CN", "section": "33.3", "signal": "term-mark", "label": "de Rham微分", "english": "de Rham differential", "offset": 584 } ], "statements": [], "resolved_references": [], "reading_order": [ "occ-d8c705dca47a1b693e25bd86", "occ-c3221aeb58474ee0a8edfdd2" ], "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": "d6c2949a1dc3b98b8110f63150825d618c1a90e7a743a0cd9f75f79ae995765c", "optional_enrichments": [] }