{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:d2085240-e280-4ce3-9875-2f28efcca408", "labels": { "zh-CN": "实标量量子场", "en": "Real scalar quantum field" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "00e295607000127b9943560114d2bf380a7de81333ce1df1912eaf8b5c362cd3", "occurrences": [ { "concept_id": "urn:uuid:d2085240-e280-4ce3-9875-2f28efcca408", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-43/04-quantization-of-the-klein-gordon-theory", "anchor": "first-a11b4a19941a57ff0903-zh", "chapter": "43", "section": "43.4", "offset": 2968, "range": [ 9990, 10785 ], "source_revision": "2ce3692d40cb8e663dd96d1a1d1fe2a58bcaf18b6ec424448ff3a56e934bfd44", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "definition", "role_basis": { "kind": "registered-source-environment", "registered_position": { "route": "books/woit-qtgr/2025-10-20/zh/chapter-43/04-quantization-of-the-klein-gordon-theory", "lang": "zh-CN", "section": "43.4", "signal": "named-definition", "label": "实标量量子场", "english": "", "offset": 2898 } }, "label": "> [!definition] 定义（实标量量子场）", "context": { "range": [ 9990, 10785 ], "quote": "\n\n> [!definition] 定义（实标量量子场）\n> 实标量量子场算符是由下式定义的算符值分布\n>\n> \n>\n> $$\n> \\widehat {\\Phi} (\\mathbf {x}) = \\frac {1}{(2 \\pi) ^ {3 / 2}} \\int_ {\\mathbf {R} ^ {3}} (a (\\mathbf {p}) e ^ {i \\mathbf {p} \\cdot \\mathbf {x}} + a ^ {\\dagger} (\\mathbf {p}) e ^ {- i \\mathbf {p} \\cdot \\mathbf {x}}) \\frac {d ^ {3} \\mathbf {p}}{\\sqrt {2 \\omega_ {\\mathbf {p}}}}\\tag{43.19}\n> $$\n>\n> \n>\n> $$\n> \\widehat {\\Pi} (\\mathbf {x}) = \\frac {1}{(2 \\pi) ^ {3 / 2}} \\int_ {\\mathbf {R} ^ {3}} (- i \\omega_ {\\mathbf {p}}) (a (\\mathbf {p}) e ^ {i \\mathbf {p} \\cdot \\mathbf {x}} - a ^ {\\dagger} (\\mathbf {p}) e ^ {- i \\mathbf {p} \\cdot \\mathbf {x}}) \\frac {d ^ {3} \\mathbf {p}}{\\sqrt {2 \\omega_ {\\mathbf {p}}}}\\tag{43.20}\n> $$\n", "quote_sha256": "e8cc0a176d834d2becfebfd25187a2d83f971f2ae9bd283aa41531469cad30cd", "environment": "definition", "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-43/04-quantization-of-the-klein-gordon-theory", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; 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