陈-西蒙斯理论 （英語：Chern–Simons theory ）以陈省身 和詹姆斯·哈里斯·西蒙斯 的名字命名，描述三维拓扑量子場論 ，在物理學有很多應用。此理論用陳-西蒙斯形式 。
陈省身 陳-西蒙斯理论描述分數量子霍爾效應 ，導致2016年的物理諾貝爾獎 。
若（G，M）是主丛 ，M是流形，G是李群 / 规范群，A是联络 ，陈西蒙斯作用量 是
S
=
k
4
π
∫
M
tr
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A
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3
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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
=
d
A
+
A
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A
{\displaystyle F=dA+A\wedge A\,}
陈西蒙斯公式 用最小作用量原理 ：
0
=
δ
S
δ
A
=
k
2
π
F
.
{\displaystyle 0={\frac {\delta S}{\delta A}}={\frac {k}{2\pi }}F.}
三维的陈-西蒙斯理论 生成很多重要的纽结多项式和纽结不变量：[ 1]
更多信息 陈西规范群G, 纽结多项式或不变量 ...
关闭
拓扑量子计算机 量子计算机 。陈西蒙斯理论陈述有些拓扑量子计算机 非阿贝尔 任意子 拓扑量子计算机 [ 2] [ 3]
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Chern, S.-S. & Simons, J. Characteristic forms and geometric invariants . Annals of Mathematics . 1974, 99 (1): 48–69. doi:10.2307/1971013 Deser, Stanley; Jackiw, Roman; Templeton, S. Three-Dimensional Massive Gauge Theories (PDF) . Physical Review Letters . 1982, 48 : 975–978 [2019-12-28 ] . Bibcode:1982PhRvL..48..975D doi:10.1103/PhysRevLett.48.975 存档 (PDF) 于2018-07-24）. Intriligator, Kenneth; Seiberg, Nathan. Aspects of 3d N = 2 Chern–Simons-Matter Theories. Journal of High Energy Physics . 2013. Bibcode:2013JHEP...07..079I arXiv:1305.1633 doi:10.1007/JHEP07(2013)079 Jackiw, Roman; Pi, S.-Y. Chern–Simons modification of general relativity. Physical Review D . 2003, 68 : 104012. Bibcode:2003PhRvD..68j4012J arXiv:gr-qc/0308071 doi:10.1103/PhysRevD.68.104012 Kulshreshtha, Usha; Kulshreshtha, D.S.; Mueller-Kirsten, H. J. W.; Vary, J. P. Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory under appropriate gauge fixing. Physica Scripta . 2009, 79 : 045001. Bibcode:2009PhyS...79d5001K doi:10.1088/0031-8949/79/04/045001 Kulshreshtha, Usha; Kulshreshtha, D.S.; Vary, J. P. Light-front Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory under appropriate gauge fixing. Physica Scripta . 2010, 82 : 055101. Bibcode:2010PhyS...82e5101K doi:10.1088/0031-8949/82/05/055101 Lopez, Ana; Fradkin, Eduardo . Fractional quantum Hall effect and Chern-Simons gauge theories. Physical Review B . 1991, 44 : 5246. Bibcode:1991PhRvB..44.5246L doi:10.1103/PhysRevB.44.5246 Marino, Marcos . Chern–Simons Theory and Topological Strings. Reviews of Modern Physics . 2005, 77 (2): 675–720. Bibcode:2005RvMP...77..675M arXiv:hep-th/0406005 doi:10.1103/RevModPhys.77.675 Marino, Marcos. Chern–Simons Theory, Matrix Models, And Topological Strings. International Series of Monographs on Physics. Oxford University Press . 2005. Witten, Edward . Topological Quantum Field Theory . Communications in Mathematical Physics . 1988, 117 : 353 [2020-09-21 ] . Bibcode:1988CMaPh.117..353W doi:10.1007/BF01223371 存档 于2017-08-25）.Witten, Edward . Quantum Field Theory and the Jones Polynomial. Communications in Mathematical Physics . 1989, 121 (3): 351–399. Bibcode:1989CMaPh.121..351W MR 0990772 doi:10.1007/BF01217730 Witten, Edward. Chern–Simons Theory as a String Theory. Progress in Mathematics . 1995, 133 : 637–678. Bibcode:1992hep.th....7094W arXiv:hep-th/9207094 
