陳-西蒙斯理論

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。 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 ( A ∧ d A + 2 3 A ∧ A ∧ A ) . {\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 ∧ 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： 拓扑量子计算机（英语：Topological quantum computer）是一种量子计算机。陈西蒙斯理论陈述有些拓扑量子计算机（英语：Topological quantum computer）的模型，例如“杨李模型”（Fibonacci model），这是最简单的非阿贝尔任意子拓扑量子计算机（英语：Topological quantum computer）之一。 陳-西蒙斯理論是最有名的拓撲量子場論之一 拓撲量子場論 Wess-Zumino-Witten模型 紐結理論 Witten, Edward. Quantum field theory and the Jones polynomial. Communications in Mathematical Physics. 1989-09, 121 (3): 351–399. ISSN 0010-3616. doi:10.1007/BF01217730 （英语）.  Freedman, Michael H.; Kitaev, Alexei; Larsen, Michael J.; Wang, Zhenghan. Topological Quantum Computation. arXiv:quant-ph/0101025. 2002-09-20 [2020-06-04]. （原始内容存档于2020-07-24）.  Wang, Zhenghan. Topological Quantum Computation (PDF). （原始内容存档 (PDF)于2017-08-30）.  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. （原始内容存档 (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. （原始内容存档于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 .