{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:217fa41e-b347-4210-af2d-3fbb37069123",
  "labels": {
    "zh-CN": "马约拉纳场算符",
    "en": "Majorana field operator"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "73144fecf665ad0eb2f989dba0c86f72d876dca45b21f926f780aa88b7ab293a",
  "occurrences": [
    {
      "concept_id": "urn:uuid:217fa41e-b347-4210-af2d-3fbb37069123",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "zh-CN",
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-47/02-majorana-spinors-and-the-majorana-field",
      "anchor": "first-34bedb23f78eb075f19e-zh",
      "chapter": "47",
      "section": "47.2",
      "offset": 11231,
      "range": [
        18645,
        19133
      ],
      "source_revision": "bde53867ea86fea1a95dec1862ffae6a442c8d1ae05be8de216cd61e539a1852",
      "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-47/02-majorana-spinors-and-the-majorana-field",
          "lang": "zh-CN",
          "section": "47.2",
          "signal": "named-definition",
          "label": "马约拉纳场算符",
          "english": "",
          "offset": 11161
        }
      },
      "label": "> [!definition] 定义（马约拉纳场算符）",
      "context": {
        "range": [
          18645,
          19133
        ],
        "quote": "\n\n> [!definition] 定义（马约拉纳场算符）\n> 马约拉纳场算符由下式给出\n>\n> $$\n> \\widehat {\\Psi} (\\mathbf {x}, t) = \\frac {1}{(2 \\pi) ^ {3 / 2}} \\int_ {\\mathbf {R} ^ {3}} \\sum_ {s = \\pm} (a _ {s} (\\mathbf {p}) u _ {s} (\\mathbf {p}) e ^ {- i \\omega_ {\\mathbf {p}} t} e ^ {i \\mathbf {p} \\cdot \\mathbf {x}} + a _ {s} ^ {\\dagger} (\\mathbf {p}) \\overline {{u _ {s} (\\mathbf {p})}} e ^ {i \\omega_ {\\mathbf {p}} t} e ^ {- i \\mathbf {p} \\cdot \\mathbf {x}}) \\frac {d ^ {3} \\mathbf {p}}{\\sqrt {2 \\omega_ {\\mathbf {p}}}}\n> $$\n",
        "quote_sha256": "7408695ccbcd304d4b11c1dd0abc78f5864182994d71ac5b56e5e56bb022e41a",
        "environment": "definition",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-47/02-majorana-spinors-and-the-majorana-field",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-b02b9ea3645aa588a1dc3489"
    },
    {
      "concept_id": "urn:uuid:217fa41e-b347-4210-af2d-3fbb37069123",
      "book_id": "woit-qtgr",
      "edition_id": "2025-10-20",
      "lang": "en",
      "route": "books/woit-qtgr/2025-10-20/en/chapter-47/02-majorana-spinors-and-the-majorana-field",
      "anchor": "first-2e9d8a043cb2513cd794-en",
      "chapter": "47",
      "section": "47.2",
      "offset": 17148,
      "range": [
        23718,
        25057
      ],
      "source_revision": "296776a837a167278bf91fa7de96c7fafcbd69faf873d2a0dcfc58b2be9f595f",
      "source_category": "machine_draft",
      "review_status": "machine-draft-not-reviewed",
      "role": "theorem",
      "role_basis": {
        "kind": "registered-source-environment",
        "registered_position": {
          "route": "books/woit-qtgr/2025-10-20/en/chapter-47/02-majorana-spinors-and-the-majorana-field",
          "lang": "en",
          "section": "47.2",
          "signal": "named-theorem",
          "label": "Majorana field operator",
          "english": "Majorana field operator",
          "offset": 17078
        }
      },
      "label": "> [!theorem] Definition (Majorana field operator)",
      "context": {
        "range": [
          23718,
          25057
        ],
        "quote": "\n\n> [!theorem] Definition (Majorana field operator)\n> The Majorana field operator is given by\n>\n> $$\n> \\widehat {\\Psi} (\\mathbf {x}, t) = \\frac {1}{(2 \\pi) ^ {3 / 2}} \\int_ {\\mathbf {R} ^ {3}} \\sum_ {s = \\pm} (a _ {s} (\\mathbf {p}) u _ {s} (\\mathbf {p}) e ^ {- i \\omega_ {\\mathbf {p}} t} e ^ {i \\mathbf {p} \\cdot \\mathbf {x}} + a _ {s} ^ {\\dagger} (\\mathbf {p}) \\overline {{u _ {s} (\\mathbf {p})}} e ^ {i \\omega_ {\\mathbf {p}} t} e ^ {- i \\mathbf {p} \\cdot \\mathbf {x}}) \\frac {d ^ {3} \\mathbf {p}}{\\sqrt {2 \\omega_ {\\mathbf {p}}}}\n> $$\n>\n> If one uses commutation instead of anticommutation relations, the Hamiltonian operator will have eigenstates with arbitrarily negative energy, and there will be problems with causality due to observable operators at space-like separated points not commuting. These two problems are resolved by the use of anticommutation instead of commutation relations. The multi-particle state space for the theory has occupation numbers 0 or 1 for each value of p and for each value of $s = \\pm$ . Like the case of the real scalar field, the particles described by these states are their own antiparticles. Unlike the case of the real scalar field, each particle state has a $\\mathbf { C } ^ { 2 }$ degree of freedom corresponding to its spin $\\begin{array} { l } { { \\frac { 1 } { 2 } } } \\end{array}$ nature.\n",
        "quote_sha256": "b1f5ec77c5ad512869f32150324caa7e3b12ca5d6f740f9396eb7d2a2ef66e2a",
        "environment": "theorem",
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "books/woit-qtgr/2025-10-20/zh/chapter-47/02-majorana-spinors-and-the-majorana-field",
          "lang": "zh-CN",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-f1664271e8aed95995357ea9"
    }
  ],
  "registered_positions": [
    {
      "route": "books/woit-qtgr/2025-10-20/en/chapter-47/02-majorana-spinors-and-the-majorana-field",
      "lang": "en",
      "section": "47.2",
      "signal": "named-theorem",
      "label": "Majorana field operator",
      "english": "Majorana field operator",
      "offset": 17078
    },
    {
      "route": "books/woit-qtgr/2025-10-20/zh/chapter-47/02-majorana-spinors-and-the-majorana-field",
      "lang": "zh-CN",
      "section": "47.2",
      "signal": "named-definition",
      "label": "马约拉纳场算符",
      "english": "",
      "offset": 11161
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-b02b9ea3645aa588a1dc3489",
    "occ-f1664271e8aed95995357ea9"
  ],
  "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": "60e41377a7e3aa0206abb0fdf8ebc047747c9f53407fdbcf1bac5097aa60b8f8",
  "optional_enrichments": []
}