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"quote": "\n\n> [!definition] 定义（$\\mathfrak{sl}(2,\\mathbb R)$ 的元辛表示）\n>\n> $\\mathcal F$ 上的表示 $\\Gamma_{BF}^{\\prime}$ 定义如下：\n>\n> $$\n> \\Gamma_ {B F} ^ {\\prime} (G) = \\Gamma_ {B F} ^ {\\prime} (X _ {+} + X _ {-}) = - \\frac {i}{2} ((a ^ {\\dagger}) ^ {2} + a ^ {2})\n> $$\n>\n> \n>\n> $$\n> \\Gamma_ {B F} ^ {\\prime} (E + F) = \\Gamma_ {B F} ^ {\\prime} (- i (X _ {+} - X _ {-})) = - \\frac {1}{2} ((a ^ {\\dagger}) ^ {2} - a ^ {2})\\tag{24.2}\n> $$\n>\n> $$\n> \\Gamma_ {B F} ^ {\\prime} (E - F) = \\Gamma_ {B F} ^ {\\prime} (Z) = - i \\frac {1}{2} (a ^ {\\dagger} a + a a ^ {\\dagger})\n> $$\n",
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