{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:52a09bf2-6b64-4f64-8d17-cb50a2c294d5", "labels": { "zh-CN": "电荷算符", "en": "charge operator" }, "alternative_labels": [ { "lang": "en", "value": "Charge operator" } ], "scope_note": "", "identity_status": "active", "identity_revision": "4657e03c7551db94a589c43fd4a61709e1570998d0578cf05df0657f1db31e36", "occurrences": [ { "concept_id": "urn:uuid:52a09bf2-6b64-4f64-8d17-cb50a2c294d5", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-02/index", "anchor": "first-bbf4d016dc21069094bf-zh", "chapter": "2", "section": "2", "offset": 2572, "range": [ 9830, 10142 ], "source_revision": "419ac63f327dd8ec1940b506658884008ceb07824f738873312b5a720d3bf3b1", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "电荷算符(charge operator)", "context": { "range": [ 9814, 10270 ], "quote": "我们有时把算符 $Q$ 称为“[电荷算符(charge operator)](../../../../../concepts/representation-theory/charge-operator)”，并赋予“电荷”一词比具体电荷更广的含义。$U ( 1 )$表示在数学中也无处不在，其中$Q$算符的整数特征值常被称为“权”。", "quote_sha256": "82ecb06c590b05e8f6ac2ec2f4529d678c1aac122745c675922e0594268c363a", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-02/index", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-5fbb158d91ced7b81cb502be" }, { "concept_id": "urn:uuid:52a09bf2-6b64-4f64-8d17-cb50a2c294d5", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-02/03-the-charge-operator", "anchor": "concept-2-charge-operator", "chapter": "2", "section": "2.3", "offset": 1622, "range": [ 10573, 10822 ], "source_revision": "7cb1477fa88eec92b663ed1fa2fbaf470545debc891586ca27b06d984f4bd895", "source_category": "translation", "review_status": "unreviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "电荷算符(charge operator)", "context": { "range": [ 10521, 11375 ], "quote": "\n> [!definition] 定义 · 电荷算符(charge operator)\n> \n>\n> 定义。对于 $U(1)$ 在 $\\mathcal H$ 上的表示 $(\\pi,\\mathcal H)$，电荷算符 $Q$ 是作用于 $\\mathcal H$ 的自伴线性算符；在每个不可约子表示 $\\mathcal H_{q_j}$ 上，它等于乘以 $q_j$。若在各 $\\mathcal H_{q_j}$ 中选取基向量，则 $Q$ 在 $\\mathcal H$ 上的矩阵为：\n>\n> \n>\n> $$\n> Q = \\left( \\begin{array}{c c c c} q _ {1} & 0 & \\dots & 0 \\\\ 0 & q _ {2} & \\dots & 0 \\\\ \\dots & & & \\dots \\\\ 0 & 0 & \\dots & q _ {n} \\end{array} \\right)\n> $$\n", "quote_sha256": "72d814ea99eb6b7498256c2cb03d8503715c4b662b79651a69f39fb2d4d3f5e3", "environment": "definition", "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-02/03-the-charge-operator", "lang": "en", "source_category": "original_transcription", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-3f1f847d463614a2cf3890d5" }, { "concept_id": "urn:uuid:52a09bf2-6b64-4f64-8d17-cb50a2c294d5", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-02/03-the-charge-operator", "anchor": "first-bbf4d016dc21069094bf-en", "chapter": "2", "section": "2.3", "offset": 2382, "range": [ 9569, 10442 ], "source_revision": "f1df7195dcbf26d7618aec589de1cdf7c5d57ce73f39e41e1413a29b7eee5f93", "source_category": "original_transcription", "review_status": "ai-transcription-compared", "role": "definition", "role_basis": { "kind": "registered-source-environment", "registered_position": { "route": "books/woit-qtgr/2025-10-20/en/chapter-02/03-the-charge-operator", "lang": "en", "section": "2.3", "signal": "named-definition", "label": "Charge operator", "english": "Charge operator", "offset": 2312 } }, "label": "> [!definition] Definition · Charge operator", "context": { "range": [ 9569, 10442 ], "quote": "\n\n> [!definition] Definition · Charge operator\n> \n>\n> \n>\n> Definition. The charge operator $Q$ for the $U ( 1 )$ representation $( \\pi , \\mathcal { H } )$ is the self-adjoint linear operator on $\\mathcal{H}$ that acts by multiplication by $q _ { j }$ on the irreducible sub-representation $\\mathcal { H } _ { q _ { j } }$ . Taking basis elements in $\\mathcal { H } _ { q _ { j } }$ it acts on $\\mathcal{H}$ as the matrix\n>\n> \n>\n> $$\n> Q = \\left( \\begin{array}{c c c c} q _ {1} & 0 & \\dots & 0 \\\\ 0 & q _ {2} & \\dots & 0 \\\\ \\dots & & & \\dots \\\\ 0 & 0 & \\dots & q _ {n} \\end{array} \\right)\n> $$\n", "quote_sha256": "24926025397844c8125d9998265251606b2296a4860653a976f4651ce93a9102", "environment": "definition", "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-02/03-the-charge-operator", "lang": "zh-CN", "source_category": "translation", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-f9700a446ae4044a0bedb2c2" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-02/index", "lang": "zh-CN", "section": "2", "signal": "term-mark", "label": "电荷算符", "english": "charge operator", "offset": 2069 }, { "route": "books/woit-qtgr/2025-10-20/en/chapter-02/03-the-charge-operator", "lang": "en", "section": "2.3", "signal": "named-definition", "label": "Charge operator", "english": "Charge operator", "offset": 2312 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-02/03-the-charge-operator", "lang": "zh-CN", "section": "2.3", "signal": "term-mark", "label": "电荷算符", "english": "charge operator", "offset": 1622 } ], "statements": [], "resolved_references": [], "reading_order": [ "occ-5fbb158d91ced7b81cb502be", "occ-3f1f847d463614a2cf3890d5", "occ-f9700a446ae4044a0bedb2c2" ], "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": "c373e3b129d0fd298a8a6c845dfbdace0f0100eeb5cde507683a344b928c8e13", "optional_enrichments": [] }