{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:e725ddcb-6d23-450c-be5a-8ec98d7f307b", "labels": { "zh-CN": "Siegel 上半空间", "en": "Siegel upper half-space" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "10d40367680106e040278472036dc09d735e15feb3551865f55074aa2fa161d3", "occurrences": [ { "concept_id": "urn:uuid:e725ddcb-6d23-450c-be5a-8ec98d7f307b", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "anchor": "first-355d3fda6fbea5309d78-zh", "chapter": "26", "section": "26.6", "offset": 1171, "range": [ 8163, 8496 ], "source_revision": "c3a9cc96f7c6dbef555811a2ad5bd45eee8efdc63abedfe8145b6bf5225a5614", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "Siegel 上半空间(Siegel upper half-space)", "context": { "range": [ 7803, 8568 ], "quote": "- 它指定一个被所有湮灭算符湮灭的特殊向量 $|0\\rangle_J\\in\\mathcal H$。在薛定谔表示 $L^2(\\mathbb R^d)$ 中，其位置波函数是式26.20的高维推广，仍为高斯函数；此时 $\\tau$ 是虚部正定的对称矩阵。这类矩阵参数化正相容复结构空间，称为“[Siegel 上半空间(Siegel upper half-space)](../../../../../concepts/symplectic-geometry/siegel-upper-half-space)”。", "quote_sha256": "fc7cd76f14f559a4cbe4f72e8f714363147374da3336cf845aae93b238648351", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-7e41de39fea464df58003658" }, { "concept_id": "urn:uuid:e725ddcb-6d23-450c-be5a-8ec98d7f307b", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "anchor": "first-355d3fda6fbea5309d78-en", "chapter": "26", "section": "26.6", "offset": 1761, "range": [ 7895, 8215 ], "source_revision": "1dabffb388c16dfb4234ff6292dfa54cae2c028fa1903605632c56764979b3da", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "Siegel upper half-space", "context": { "range": [ 7285, 8287 ], "quote": "- As a distinguished vector $|0\\rangle_J\\in\\mathcal H$, annihilated by all annihilation operators. Its position-space wavefunction in the Schrödinger representation $L^2(\\mathbb R^d)$ is a Gaussian generalizing equation 26.20, with $\\tau$ now a symmetric matrix with positive-definite imaginary part. These matrices parametrize the space of positive compatible complex structures, called the “[Siegel upper half-space](../../../../../concepts/symplectic-geometry/siegel-upper-half-space)”.", "quote_sha256": "7666f84be512f05470294de5aafd5f2dcb3bdd7a64f30756eda4bff8c48b50f6", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-7f320ff7b02245c94ea63268" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "lang": "en", "section": "26.6", "signal": "term-mark", "label": "Siegel upper half-space", "english": "Siegel upper half-space", "offset": 1605 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "lang": "zh-CN", "section": "26.6", "signal": "term-mark", "label": "Siegel 上半空间", "english": "Siegel upper half-space", "offset": 1015 } ], "statements": [], "resolved_references": [ { "raw": "href=\"05-complex-structures-for-d-1-and-squeezed-states#equation-26-20\"", "href": "05-complex-structures-for-d-1-and-squeezed-states#equation-26-20", "range": [ 7890, 7961 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/zh/chapter-26/05-complex-structures-for-d-1-and-squeezed-states", "target_anchor": "equation-26-20", "resolved": true, "reason": null, "source_revision": "c3a9cc96f7c6dbef555811a2ad5bd45eee8efdc63abedfe8145b6bf5225a5614", "source_route": "books/woit-qtgr/2025-10-20/zh/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "occurrence_id": "occ-7e41de39fea464df58003658" }, { "raw": "href=\"05-complex-structures-for-d-1-and-squeezed-states#equation-26-20\"", "href": "05-complex-structures-for-d-1-and-squeezed-states#equation-26-20", "range": [ 7499, 7570 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-26/05-complex-structures-for-d-1-and-squeezed-states", "target_anchor": "equation-26-20", "resolved": true, "reason": null, "source_revision": "1dabffb388c16dfb4234ff6292dfa54cae2c028fa1903605632c56764979b3da", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-26/06-complex-structures-and-bargmann-fock-quantization-for-arbitrary-d", "occurrence_id": "occ-7f320ff7b02245c94ea63268" } ], "reading_order": [ "occ-7e41de39fea464df58003658", "occ-7f320ff7b02245c94ea63268" ], "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": "6f0358537c1bbb84fa07139ae6ac620d4f85a6f688f358fc9883f648fa651905", "optional_enrichments": [] }