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        "quote": "- 第一个群在 $\\mathbf{C}^2$ 上的表示，最容易看作 $\\mathrm{SU}(2)$ 的[<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/defining-representation\" data-concept-identity=\"urn:uuid:6800cca5-05b3-4571-9b98-979ca6c8a5c1\" data-concept-route=\"/concept-identities#concept-6800cca5-05b3-4571-9b98-979ca6c8a5c1\">定义表示(defining representation)</u>](../../../../../concepts/representation-theory/defining-representation)。它不是 $\\mathrm{SO}(3)$ 的表示：从单位元出发，沿不可收缩回路绕行一周后，该回路在 $\\mathrm{SU}(2)$ 中的提升会到达负单位元，而非单位元，因此这种作用不能下降为 $\\mathrm{SO}(3)$ 的表示。这称为“[<u id=\"concept-6-3-spinor-representation\" class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/spinor-representation\" data-concept-id=\"concept-6-3-spinor-representation\" data-concept-identity=\"urn:uuid:8d16bffc-ce2e-49f4-9683-6eabeb80e54b\" data-concept-route=\"/concept-identities#concept-8d16bffc-ce2e-49f4-9683-6eabeb80e54b\">自旋 1/2 表示(spin-1/2 representation)</u>](../../../../../concepts/representation-theory/spinor-representation)”或“[<u class=\"concept-term\" data-concept-reference=\"concepts/representation-theory/spinor-representation\" data-concept-identity=\"urn:uuid:9784dcc7-9e6e-4545-b544-9c8e88f90bf7\" data-concept-route=\"/concept-identities#concept-9784dcc7-9e6e-4545-b544-9c8e88f90bf7\" id=\"first-a5b0282092358cde57b2-zh\">旋量表示(spinor representation)</u>](../../../../../concepts/representation-theory/spinor-representation)”，并将在[第 7 章](../chapter-07/index#section-7)中进一步讨论。",
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