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        "quote": "实验观察到的一个事实是，自旋为 $\\frac { 1 } { 2 }$ 的基本粒子表现为费米子，并由费米子场描述。在非相对论量子场论中，这种自旋为 $\\textstyle { \\frac { 1 } { 2 } }$ 的基本粒子原则上可以是玻色子，由<a href=\"05-spatial-symmetries#section-38-3-3\" class=\"cross-reference\" id=\"xref-09-fermionic-fields-1\" data-reference=\"section-38-3-3\">第 38.3.3 节</a>中的玻色子场描述。然而，在相对论量子场论中存在一个 a “[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-field-theory/spin-statistics-theorem\" data-concept-identity=\"urn:uuid:b087a1f3-81a9-4c70-a5b6-29950378bdd0\" data-concept-route=\"/concept-identities#concept-b087a1f3-81a9-4c70-a5b6-29950378bdd0\" id=\"first-d0a75f032e011568a30c-zh\">自旋–统计定理(spin-statistics theorem)</u>](../../../../../concepts/quantum-field-theory/spin-statistics-theorem)”，它指出自旋为 $\\frac12$ 的域必须用反对易子量子化。这为观察到的自旋值与粒子统计之间的关联提供了解释，原因在于描述基本粒子的非相对论理论应当是相对论理论的低能极限。",
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        "quote": "It is an experimentally observed fact that elementary particles with spin $\\frac { 1 } { 2 }$ behave as fermions and are described by fermionic fields. In non-relativistic quantum field theory, such spin $\\textstyle { \\frac { 1 } { 2 } }$ elementary particles could in principle be bosons, described by bosonic fields as in <a href=\"05-spatial-symmetries#section-38-3-3\" class=\"cross-reference\" id=\"xref-09-fermionic-fields-1\" data-reference=\"section-38-3-3\">section 38.3.3</a>. There is however a “[<u class=\"concept-term\" data-concept-reference=\"concepts/quantum-field-theory/spin-statistics-theorem\" data-concept-identity=\"urn:uuid:b087a1f3-81a9-4c70-a5b6-29950378bdd0\" data-concept-route=\"/concept-identities#concept-b087a1f3-81a9-4c70-a5b6-29950378bdd0\" id=\"first-d0a75f032e011568a30c-en\">spin-statistics theorem</u>](../../../../../concepts/quantum-field-theory/spin-statistics-theorem)” in relativistic quantum field theory that says that spin $\\frac12$ fields must be quantized with anticommutators. This provides an explanation of the observed correlation of values of the spin and of the particle statistics, due to the fact that the non-relativistic theories describing fundamental particles should be low-energy limits of relativistic theories.",
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