{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:9d30f001-86e0-4e06-9631-c199d9cc5ae4",
  "labels": {
    "zh-CN": "费米子Fock空间",
    "en": "fermionic Fock space"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "83c4aae61b4186a0dbcbaec89037b64be1a8ad2e4a00db709abcb0d28dfb5e8c",
  "occurrences": [
    {
      "concept_id": "urn:uuid:9d30f001-86e0-4e06-9631-c199d9cc5ae4",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/04-spinors-and-the-bargmann-fock-construction",
      "anchor": "first-1c8d82155046b0e8ad06-zh",
      "chapter": "31",
      "section": "31.3",
      "offset": 3737,
      "range": [
        11243,
        11566
      ],
      "source_revision": "8ee5a6e2f5207bfb3627c5b8de45de2af37ceeec1dfb290aac03caac7de9aab1",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "费米子Fock空间(fermionic Fock space)",
      "context": {
        "range": [
          10904,
          11660
        ],
        "quote": "其中 $f _ { 1 }$ 和 $f _ { 2 }$ 是反交换变量 $\\theta _ { j }$ 的各次幂的复线性组合。关于此内积构造的细节，见 [91] 的第 7.2 章或 [110] 的第 7.5 章和<a href=\"../chapter-07/06-for-further-reading#section-7-6\" class=\"cross-reference\" id=\"xref-04-spinors-and-the-bargmann-fock-construction-1\" data-reference=\"section-7-6\">第 7.6</a> 章。我们将把这个态空间记作 $\\mathcal { F } _ { d } ^ { + }$，并称之为[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/fermionic-fock-space\" data-concept-identity=\"urn:uuid:9d30f001-86e0-4e06-9631-c199d9cc5ae4\" data-concept-route=\"/concept-identities#concept-9d30f001-86e0-4e06-9631-c199d9cc5ae4\" id=\"first-1c8d82155046b0e8ad06-zh\">费米子Fock空间(fermionic Fock space)</u>](../../../../../concepts/quantum-mechanics/fermionic-fock-space)。由于它是有限维的，因此不需要像玻色子情形那样进行完备化。",
        "quote_sha256": "13f2d8fa8eeb11987911b082ab2dc8b4b9ddd9175b470dc812c09d9123b64359",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-31/04-spinors-and-the-bargmann-fock-construction",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-c90f510fb15aeaed61087d4b"
    },
    {
      "concept_id": "urn:uuid:9d30f001-86e0-4e06-9631-c199d9cc5ae4",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/04-spinors-and-the-bargmann-fock-construction",
      "anchor": "first-1c8d82155046b0e8ad06-en",
      "chapter": "31",
      "section": "31.3",
      "offset": 5309,
      "range": [
        11965,
        12277
      ],
      "source_revision": "b708adccd888d3e8e8b32c1aeb70eef369f6f3f6465833cd33415f2ee70a28d5",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "fermionic Fock space",
      "context": {
        "range": [
          11626,
          12433
        ],
        "quote": "where $f _ { 1 }$ and $f _ { 2 }$ are complex linear combinations of the powers of the anticommuting variables $\\theta _ { j }$ . For the details of the construction of this inner product, see chapter 7.2 of [91] or chapters 7.5 and 7.6 of [110]. We will denote this state space as $\\mathcal { F } _ { d } ^ { + }$ and refer to it as the [<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/fermionic-fock-space\" data-concept-identity=\"urn:uuid:9d30f001-86e0-4e06-9631-c199d9cc5ae4\" data-concept-route=\"/concept-identities#concept-9d30f001-86e0-4e06-9631-c199d9cc5ae4\" id=\"first-1c8d82155046b0e8ad06-en\">fermionic Fock space</u>](../../../../../concepts/quantum-mechanics/fermionic-fock-space). Since it is finite dimensional, there is no need for a completion as in the bosonic case.",
        "quote_sha256": "8f17906e6ef730df895d52e5a788133973ab5840802fbceaf427beb9e5418b8c",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/04-spinors-and-the-bargmann-fock-construction",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-392a33ff37f45af60849d87d"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-31/04-spinors-and-the-bargmann-fock-construction",
      "lang": "en",
      "section": "31.3",
      "signal": "term-mark",
      "label": "fermionic Fock space",
      "english": "fermionic Fock space",
      "offset": 5309
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-31/04-spinors-and-the-bargmann-fock-construction",
      "lang": "zh-CN",
      "section": "31.3",
      "signal": "term-mark",
      "label": "费米子Fock空间",
      "english": "fermionic Fock space",
      "offset": 3737
    }
  ],
  "statements": [],
  "resolved_references": [
    {
      "raw": "href=\"../chapter-07/06-for-further-reading#section-7-6\"",
      "href": "../chapter-07/06-for-further-reading#section-7-6",
      "range": [
        11014,
        11069
      ],
      "relation": "references",
      "target_route": "books/woit-qtgr/2025-10-20/zh/chapter-07/06-for-further-reading",
      "target_anchor": "section-7-6",
      "resolved": true,
      "reason": null,
      "source_revision": "8ee5a6e2f5207bfb3627c5b8de45de2af37ceeec1dfb290aac03caac7de9aab1",
      "source_route": "books/woit-qtgr/2025-10-20/zh/chapter-31/04-spinors-and-the-bargmann-fock-construction",
      "occurrence_id": "occ-c90f510fb15aeaed61087d4b"
    }
  ],
  "reading_order": [
    "occ-c90f510fb15aeaed61087d4b",
    "occ-392a33ff37f45af60849d87d"
  ],
  "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": "84af449a757be272806e755afa1dfd32b3b71430882eaf250060ef40fb426fe0",
  "optional_enrichments": []
}
