陳-施蒙斯理論 (英語:Chern–Simons theory )以陳省身 和占士·夏里斯·施蒙斯 的名字命名,描述三維拓撲量子場論 ,在物理學有很多應用。此理論用陳-施蒙斯形式 。
陳省身
陳-施蒙斯理論描述分數量子霍爾效應 ,導致2016年的物理諾貝爾獎 。
若(G,M)是主叢 ,M是流形,G是李群 / 規範群,A是聯絡 ,陳施蒙斯作用量 是
S
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k
4
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A
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A
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{\displaystyle S={\frac {k}{4\pi }}\int _{M}{\text{tr}}\,(A\wedge dA+{\tfrac {2}{3}}A\wedge A\wedge A).}
F是曲率:
F
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d
A
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A
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A
{\displaystyle F=dA+A\wedge A\,}
陳施蒙斯公式 用最小作用量原理 :
0
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δ
S
δ
A
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k
2
π
F
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{\displaystyle 0={\frac {\delta S}{\delta A}}={\frac {k}{2\pi }}F.}
三維的陳-施蒙斯理論 生成很多重要的紐結多項式和紐結不變量:[ 1]
More information 陳西規範群G, 紐結多項式或不變量 ...
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拓撲量子計算機 是一種量子計算機 。陳施蒙斯理論陳述有些拓撲量子計算機 的模型,例如「楊李模型」(Fibonacci model),這是最簡單的非阿貝爾 任意子 拓撲量子計算機 之一。[ 2] [ 3]
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