查看“︁陳-西蒙斯理論”︁的源代码

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'''陈-西蒙斯理论'''（{{lang-en|Chern–Simons theory}}）以[[陈省身]]和[[詹姆斯·西蒙斯|詹姆斯·哈里斯·西蒙斯]]的名字命名，描述三维[[拓撲量子場論|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]]。
[[File:Shiing-Shen Chern 2.jpg|缩略图|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]]。

== 經典公式 ==
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

:<math>S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A).</math>

F是曲率：

:<math>F = dA + A \wedge A \, </math>

'''陈西蒙斯公式'''用[[最小作用量原理]]：

:<math>0=\frac{\delta S}{\delta A}=\frac{k}{2\pi} F.</math>

== 陈-西蒙斯理论和纽结多项式 ==
{{Main|纽结多项式}}三维的[[陳-西蒙斯理論|陈-西蒙斯理论]]生成很多重要的纽结多项式和纽结不变量：<ref>{{Cite journal|title=Quantum field theory and the Jones polynomial|url=http://link.springer.com/10.1007/BF01217730|last=Witten|first=Edward|date=1989-09|journal=Communications in Mathematical Physics|issue=3|doi=10.1007/BF01217730|volume=121|pages=351–399|language=en|issn=0010-3616}}</ref>
{| class="wikitable"
|+[[陈西理论]]的纽结拓扑不变量
!陈西规范群G
!纽结多项式或不变量
|-
|[[SO(n)|SO(N)]]
|[[考夫曼多項式]]
|-
|[[SU(n)|SU(N)]]
|[[HOMFLY多項式]]
|-
|SU(2)或SO(3)
|[[琼斯多项式|鍾斯多項式]]（跟[[括號多項式]]有关）
|-
|U(1)
|[[环绕数]]
|}

== 拓扑量子计算机 ==
{{En-link|拓扑量子计算机|Topological quantum computer}}是一种[[量子计算机]]。陈西蒙斯理论陈述有些{{En-link|拓扑量子计算机|Topological quantum computer}}的模型，例如“杨李模型”（Fibonacci model），这是最简单的[[非阿贝尔群|非阿贝尔]][[任意子]]{{En-link|拓扑量子计算机|Topological quantum computer}}之一。<ref>{{Cite journal|title=Topological Quantum Computation|url=http://arxiv.org/abs/quant-ph/0101025|last=Freedman|first=Michael H.|last2=Kitaev|first2=Alexei|date=2002-09-20|journal=arXiv:quant-ph/0101025|last3=Larsen|first3=Michael J.|last4=Wang|first4=Zhenghan|access-date=2020-06-04|archive-date=2020-07-24|archive-url=https://web.archive.org/web/20200724223421/https://arxiv.org/abs/quant-ph/0101025|dead-url=no}}</ref><ref>{{Cite web|title=Topological Quantum Computation|url=http://web.math.ucsb.edu/~zhenghwa/data/course/cbms.pdf|date=|last=Wang|first=Zhenghan|archive-url=https://web.archive.org/web/20170830033325/http://web.math.ucsb.edu/~zhenghwa/data/course/cbms.pdf|archive-date=2017-08-30|access-date=|website=|dead-url=no}}</ref>

== 參見 ==

* 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]]

== 参考文献 ==
{{Reflist}}

== 阅读 ==
* {{Cite journal|title=Characteristic forms and geometric invariants|url=https://archive.org/details/sim_annals-of-mathematics_1974-01_99_1/page/48|last=Chern|first=S.-S.|last2=Simons|first2=J.|journal=[[Annals of Mathematics]]|issue=1|doi=10.2307/1971013|year=1974|volume=99|pages=48–69|lastauthoramp=yes}}
* {{Cite journal|title=Three-Dimensional Massive Gauge Theories|url=https://authors.library.caltech.edu/85895/1/PhysRevLett.48.975.pdf|last=Deser|first=Stanley|last2=Jackiw|first2=Roman|journal=[[Physical Review Letters]]|doi=10.1103/PhysRevLett.48.975|year=1982|volume=48|pages=975–978|bibcode=1982PhRvL..48..975D|ref=harv|last3=Templeton|first3=S.|access-date=2019-12-28|archive-date=2018-07-24|archive-url=https://web.archive.org/web/20180724233616/https://authors.library.caltech.edu/85895/1/PhysRevLett.48.975.pdf|dead-url=no}}
* {{Cite journal|title=Aspects of 3d ''N''&nbsp;=&nbsp;2 Chern–Simons-Matter Theories|last=Intriligator|first=Kenneth|last2=Seiberg|first2=Nathan|journal=[[Journal of High Energy Physics]]|doi=10.1007/JHEP07(2013)079|year=2013|arxiv=1305.1633|bibcode=2013JHEP...07..079I|ref=harv}}
* {{Cite journal|title=Chern–Simons modification of general relativity|last=Jackiw|first=Roman|last2=Pi|first2=S.-Y|journal=[[Physical Review D]]|doi=10.1103/PhysRevD.68.104012|year=2003|volume=68|pages=104012|arxiv=gr-qc/0308071|bibcode=2003PhRvD..68j4012J|ref=harv}}
* {{Cite journal|title=Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory under appropriate gauge fixing|last=Kulshreshtha|first=Usha|last2=Kulshreshtha|first2=D.S.|journal=[[Physica Scripta ]]|doi=10.1088/0031-8949/79/04/045001|year=2009|volume=79|pages=045001|bibcode=2009PhyS...79d5001K|last3=Mueller-Kirsten|first3=H. J. W.|last4=Vary|first4=J. P.}}
* {{Cite journal|title=Light-front Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory under appropriate gauge fixing|last=Kulshreshtha|first=Usha|last2=Kulshreshtha|first2=D.S.|journal=[[Physica Scripta]]|doi=10.1088/0031-8949/82/05/055101|year=2010|volume=82|pages=055101|bibcode=2010PhyS...82e5101K|last3=Vary|first3=J. P.}}
* {{Cite journal|title=Fractional quantum Hall effect and Chern-Simons gauge theories|last=Lopez|first=Ana|last2=Fradkin|first2=Eduardo|authorlink2=Eduardo Fradkin|journal=[[Physical Review B]]|doi=10.1103/PhysRevB.44.5246|year=1991|volume=44|pages=5246|bibcode=1991PhRvB..44.5246L|ref=harv}}
* {{Cite journal|title=Chern–Simons Theory and Topological Strings|last=Marino|first=Marcos|authorlink=Marcos Marino|journal=[[Reviews of Modern Physics]]|issue=2|doi=10.1103/RevModPhys.77.675|year=2005|volume=77|pages=675–720|arxiv=hep-th/0406005|bibcode=2005RvMP...77..675M}}
* {{Cite book|first=Marcos|last=Marino|title=Chern–Simons Theory, Matrix Models, And Topological Strings|series=International Series of Monographs on Physics|publisher=[[Oxford University Press]]|year=2005}}
* {{Cite journal|title=Topological Quantum Field Theory|url=http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.cmp/1104161738|last=Witten|first=Edward|authorlink=Edward Witten|journal=[[Communications in Mathematical Physics]]|doi=10.1007/BF01223371|year=1988|volume=117|pages=353|bibcode=1988CMaPh.117..353W|access-date=2020-09-21|archive-date=2017-08-25|archive-url=https://web.archive.org/web/20170825062712/https://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.cmp%2F1104161738|dead-url=no}}
* {{Cite journal|title=Quantum Field Theory and the Jones Polynomial|last=Witten|first=Edward|authorlink=Edward Witten|journal=[[Communications in Mathematical Physics]]|issue=3|doi=10.1007/BF01217730|year=1989|volume=121|pages=351–399|bibcode=1989CMaPh.121..351W|mr=0990772}}
* {{Cite journal|title=Chern–Simons Theory as a String Theory|last=Witten|first=Edward|journal=[[Progress in Mathematics]]|issue=|year=1995|volume=133|pages=637–678|arxiv=hep-th/9207094|bibcode=1992hep.th....7094W}}

{{Quantum field theory}}
{{String theory}}
{{纽结理论}}
[[Category:陈省身]]
[[Category:量子场论]]
[[Category:陈-西蒙斯理论]]