{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:3e50e9ae-4157-4eea-a762-f943f292b9b2", "labels": { "zh-CN": "二次量子化", "en": "second quantization" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "61d3dd71a760f4fffe6cbcb0972db026fc445303e130f091789ee3d93039b3a6", "occurrences": [ { "concept_id": "urn:uuid:3e50e9ae-4157-4eea-a762-f943f292b9b2", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-36/01-multi-particle-quantum-systems-as-quanta-of-a-harmonic-oscillator", "anchor": "first-71b2f278d512fe650237-zh", "chapter": "36", "section": "36.1", "offset": 4269, "range": [ 12708, 13025 ], "source_revision": "8c52a6767e57bacc208e4635f9dfb6e3600669f2758ceae75c54f05329374124", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "二次量子化(second quantization)", "context": { "range": [ 12485, 13261 ], "quote": "比较36.1与36.3，我们看到，如果$\\mathcal { H } _ { 1 } = \\mathcal { M } _ { J } ^ { + }$，则它们是相同的态空间。这种通过取经典相空间$M$的对偶为波动方程的解空间、然后用Bargmann-Fock方法量子化来构造多粒子态的方法，其中$\\mathcal { H } _ { 1 } = \\mathcal { M } _ { J } ^ { + }$是单粒子的量子态空间，有时被称为“[二次量子化(second quantization)](../../../../../concepts/quantum-mechanics/second-quantization)”。选取$\\mathcal { H } _ { 1 }$的一个（复）基，对每个基元素都得到一个独立的量子谐振子，相应的占据数就是由该基元素标记的“量子”的数目。这种形式体系自动蕴含了量子的不可区分性以及量子交换下的对称性，因为态的描述中只出现量子的数目。在通常的用量子力学通过张量积描述多个全同粒子的方法中所需的单独对称性公设，在这里不再需要。", "quote_sha256": "af984fee3a6999ca4e9410199cefd8dc8356a5b8289d214795c1a505c36263b8", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-36/01-multi-particle-quantum-systems-as-quanta-of-a-harmonic-oscillator", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-c497b7e019d0633db9f0129b" }, { "concept_id": "urn:uuid:3e50e9ae-4157-4eea-a762-f943f292b9b2", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-36/01-multi-particle-quantum-systems-as-quanta-of-a-harmonic-oscillator", "anchor": "first-71b2f278d512fe650237-en", "chapter": "36", "section": "36.1", "offset": 6690, "range": [ 14282, 14592 ], "source_revision": "6a1cc75a76f74d12efc85d1c58309b49b72e29e85778c617ae11d9fe58b45ddb", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "second quantization", "context": { "range": [ 13845, 15226 ], "quote": "Comparing 36.1 and 36.3, we see that these are the same state spaces if $\\mathcal { H } _ { 1 } = \\mathcal { M } _ { J } ^ { + }$ This construction of multi-particle states by taking as dual classical phase space $M$ a space of solutions to a wave equation, then quantizing by the Bargmann-Fock method, with $\\mathcal { H } _ { 1 } = \\mathcal { M } _ { J } ^ { + }$ the quantum state space for a single particle, is sometimes known as “[second quantization](../../../../../concepts/quantum-mechanics/second-quantization)”. Choosing a (complex) basis of $\\mathcal { H } _ { 1 }$ , for each basis element one gets an independent quantum harmonic oscillator, with corresponding occupation number the number of “quanta” labeled by that basis element. This formalism automatically implies indistinguishability of quanta and symmetry under interchange of quanta since only the numbers of quanta appear in the description of the state. 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