"Chern-Simons gauge theory and Witten's invariant"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 Chern-Simons gauge theory and invariant로 바꾸었습니다.) |
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| 4번째 줄: | 4번째 줄: | ||
* CS is an invariant for 3-manifolds | * CS is an invariant for 3-manifolds | ||
* [[Kashaev's volume conjecture|Kashaev Volume conjecture]] | * [[Kashaev's volume conjecture|Kashaev Volume conjecture]] | ||
| − | + | * action<br> Let <math>A</math> be a SU(2)-<br><math>S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])</math><br> | |
| − | * action<br><math>S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])</math><br> | ||
| 121번째 줄: | 120번째 줄: | ||
<h5>articles</h5> | <h5>articles</h5> | ||
| − | * http://journal.ms.u-tokyo.ac.jp/pdf/jms030310.pdf | + | * [http://journal.ms.u-tokyo.ac.jp/pdf/jms030310.pdf ]http://journal.ms.u-tokyo.ac.jp/pdf/jms030310.pdf |
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* [http://www.math.columbia.edu/%7Eneumann/preprints/cs2.pdf Rationality problems for K-theory and Chern-Simons invariants of hyperbolic 3-manifolds]<br> | * [http://www.math.columbia.edu/%7Eneumann/preprints/cs2.pdf Rationality problems for K-theory and Chern-Simons invariants of hyperbolic 3-manifolds]<br> | ||
** Walter Neumann, 1995 | ** Walter Neumann, 1995 | ||
| + | * Witten, Edward. 1992. “Chern-Simons Gauge Theory As A String Theory”. <em>hep-th/9207094</em> (7월 28). http://arxiv.org/abs/hep-th/9207094.<br> | ||
* [[2010년 books and articles|논문정리]] | * [[2010년 books and articles|논문정리]] | ||
* http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4= | * http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4= | ||
2011년 9월 22일 (목) 11:18 판
introduction
- 3D TQFT( Chern-Simons theory)
- CS is an invariant for 3-manifolds
- Kashaev Volume conjecture
- action
Let \(A\) be a SU(2)-
\(S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])\)
Morse theory approach
- Taubes, Floer interpret the Chern-Simons function as a Morse function on the space of all gauge fields modulo the action of the group of gauge transformations
- analogous to Euler characteristic of a manifold can be computed as the signed count of Morse indices
Chern-Simons and arithmetic
The Chern-Simons invariants of a closed 3-manifold are secondary characteristic numbers that are given in terms of a finite set of phases in the unit circle. Hyperbolic 3-dimensional geometry links these phases with arithmetic, and identifies them with values of the Rogers dilogarithm at algebraic numbers. The quantization of these invariants are the famous Witten-Reshetikhin-Turaev invariants of 3-manifolds, constructed by the Jones polynomial. In the talk we will review conjectures regarding the asymptotics of the quantum 3-manifold invariants, and their relation to Chern-Simons theory and arithmetic. We will review progress on those conjectures, theoretical, and experimental.
Garoufalidis, Stavros. 2007. “Chern-Simons theory, analytic continuation and arithmetic”. 0711.1716 (11월 12). http://arxiv.org/abs/0711.1716
memo
history
books
- 찾아볼 수학책
- http://gigapedia.info/1/chern+simons
- http://gigapedia.info/1/wzw
- http://gigapedia.info/1/Wess+zumino
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Chern–Simons_theory
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
blogs
- 구글 블로그 검색
expositions
- An Introduction to Chern-Simons Theory
- Lie groups and Chern-Simons Theory Benjamin Himpel
- Labastida, J. M. F. 1999. “Chern-Simons Gauge Theory: Ten Years After”. hep-th/9905057 (5월 8). doi:doi:10.1063/1.59663. http://arxiv.org/abs/hep-th/9905057.
articles
- Rationality problems for K-theory and Chern-Simons invariants of hyperbolic 3-manifolds
- Walter Neumann, 1995
- Witten, Edward. 1992. “Chern-Simons Gauge Theory As A String Theory”. hep-th/9207094 (7월 28). http://arxiv.org/abs/hep-th/9207094.
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/
experts on the field