{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:3e11a671-c004-44f2-8d6e-bf7933e08bbb", "labels": { "zh-CN": "自旋", "en": "spin" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "daac7137181cb3629403e39569e91750ebc609d9846215cd37f8e535d7a11d21", "occurrences": [ { "concept_id": "urn:uuid:3e11a671-c004-44f2-8d6e-bf7933e08bbb", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "anchor": "concept-7-spin", "chapter": "7", "section": "7.2", "offset": 1276, "range": [ 11487, 11699 ], "source_revision": "af42ca8c868bc2cdc5dca3ef8a46b1cd266fae227aaba16f410d9185fd6d5068", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "自旋(spin)", "context": { "range": [ 10570, 12155 ], "quote": "在[第3](../chapter-03/index#section-3)章中我们看到，一个具有$\\mathcal { H } = \\mathbf { C } ^ { 2 }$的一般量子系统可以通过$U ( 2 )$在$\\mathbf { C } ^ { 2 }$上的作用来理解。自伴算符所表示的[可观测量(quantum observable)](../../../../../concepts/quantum-mechanics/quantum-observable)对应于相应的[李代数表示(Lie algebra representation)](../../../../../concepts/lie-theory/lie-algebra-representation)（相差一个因子 $i$）。$U ( 1 ) \\subset U ( 2 )$子群与所有其他部分对易，可以单独分析，这里我们只考虑$S U ( 2 )$子群。对于任意这样的系统，群$S U ( 2 )$没有特别的几何意义。当它作为旋转群的双覆盖出现时，称该量子系统携带[自旋(spin)](../../../../../concepts/quantum-mechanics/spin)；特别是，二维[不可约表示(irreducible representation)](../../../../../concepts/representation-theory/irreducible-representation)对应自旋 $1/2$（在[第8](../chapter-08/index#section-8)章中我们将讨论更高自旋值的态空间）。", "quote_sha256": "bea19e7f8e582a2debf5cfa5f768900e3bf495ead24a1dc72da433a2c33b9b21", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; 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Here $\\widehat{\\mathbf L}$ comprises two copies of equation38.12, induced by spatial rotations of the solutions. The [spin](../../../../../concepts/quantum-mechanics/spin-angular-momentum) operator $\\widehat{\\mathbf S}$ comes from the $SU(2)$ action on the $\\mathbb C^2$ factor and is", "quote_sha256": "b323c6e7af3cc9e6ad23c8dbd18cc50150ff2088cea5df1e4761b629902af38a", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-38/05-spatial-symmetries", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-2c161ec6dd1997507a6ffd78" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "en", "section": "7.2", "signal": "term-mark", "label": "spin", "english": "spin", "offset": 1247 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "lang": "zh-CN", "section": "7.2", "signal": "term-mark", "label": "自旋", "english": "spin", "offset": 964 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-07/03-the-heisenberg-picture", "lang": "zh-CN", "section": "7.3", "signal": "term-mark", "label": "自旋", "english": "spin", "offset": 4575 }, { "route": "books/woit-qtgr/2025-10-20/en/chapter-38/05-spatial-symmetries", "lang": "en", "section": "38.3", "signal": "term-mark", "label": "spin", "english": "spin", "offset": 13508 } ], "statements": [], "resolved_references": [ { "raw": "[第3](../chapter-03/index#section-3)", "href": "../chapter-03/index#section-3", "range": [ 10571, 10606 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/zh/chapter-03/index", "target_anchor": "section-3", "resolved": true, "reason": null, "source_revision": "af42ca8c868bc2cdc5dca3ef8a46b1cd266fae227aaba16f410d9185fd6d5068", "source_route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "occurrence_id": "occ-7a60a3fd77b212ced19c7b63" }, { "raw": "[第8](../chapter-08/index#section-8)", "href": "../chapter-08/index#section-8", "range": [ 12102, 12137 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/zh/chapter-08/index", "target_anchor": "section-8", "resolved": true, "reason": null, "source_revision": "af42ca8c868bc2cdc5dca3ef8a46b1cd266fae227aaba16f410d9185fd6d5068", "source_route": "books/woit-qtgr/2025-10-20/zh/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "occurrence_id": "occ-7a60a3fd77b212ced19c7b63" }, { "raw": "[chapter 3](../chapter-03/index#section-3)", "href": "../chapter-03/index#section-3", "range": [ 9713, 9755 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-03/index", "target_anchor": "section-3", "resolved": true, "reason": null, "source_revision": "2f4e030ded93d226da1b050014630cb67a384fcab12bb0f30e051144b3d12eec", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "occurrence_id": "occ-9afdcc6b9e05bfb6db23a0dd" }, { "raw": "[chapter 8](../chapter-08/index#section-8)", "href": "../chapter-08/index#section-8", "range": [ 11536, 11578 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-08/index", "target_anchor": "section-8", "resolved": true, "reason": null, "source_revision": "2f4e030ded93d226da1b050014630cb67a384fcab12bb0f30e051144b3d12eec", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-07/02-the-spin-half-particle-in-a-magnetic-field", "occurrence_id": "occ-9afdcc6b9e05bfb6db23a0dd" }, { "raw": "href=\"#equation-38-12\"", "href": "#equation-38-12", "range": [ 20666, 20688 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-38/05-spatial-symmetries", "target_anchor": "equation-38-12", "resolved": true, "reason": null, "source_revision": "ef4c4e6fcd9d2bfabeb07519ed46877b9a874f27c442358387b8e703b416b833", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-38/05-spatial-symmetries", "occurrence_id": "occ-2c161ec6dd1997507a6ffd78" } ], "reading_order": [ "occ-7a60a3fd77b212ced19c7b63", "occ-9afdcc6b9e05bfb6db23a0dd", "occ-3e0c61d4711f36de2bd122d1", "occ-2c161ec6dd1997507a6ffd78" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 4, "located_occurrences": 4, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "d72a4d65f5297262b32d57eb9366c23f8912e2ed93d9f679eac7168a49e39fb6", "optional_enrichments": [] }