"Vector valued differential forms"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
encyclopedia==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
||
| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
| 7번째 줄: | 7번째 줄: | ||
| − | ==exercise from Chern-Simons theory | + | ==exercise from Chern-Simons theory== |
* [[Chern-Simons gauge theory and invariant|Chern-Simons invariant]]<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> | * [[Chern-Simons gauge theory and invariant|Chern-Simons invariant]]<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> | ||
| 39번째 줄: | 39번째 줄: | ||
| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 47번째 줄: | 47번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[Knizhnik–Zamolodchikov equations(KZ equations)]] | * [[Knizhnik–Zamolodchikov equations(KZ equations)]] | ||
| 55번째 줄: | 55번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* http://en.wikipedia.org/wiki/Vector-valued_form | * http://en.wikipedia.org/wiki/Vector-valued_form | ||
| 67번째 줄: | 67번째 줄: | ||
| − | ==books | + | ==books== |
| 79번째 줄: | 79번째 줄: | ||
| − | ==expositions | + | ==expositions== |
| 87번째 줄: | 87번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles== |
| 103번째 줄: | 103번째 줄: | ||
| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
| 115번째 줄: | 115번째 줄: | ||
| − | ==blogs | + | ==blogs== |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 126번째 줄: | 126번째 줄: | ||
| − | ==experts on the field | + | ==experts on the field== |
* http://arxiv.org/ | * http://arxiv.org/ | ||
| 134번째 줄: | 134번째 줄: | ||
| − | ==links | + | ==links== |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 15:57 판
introduction
exercise from Chern-Simons theory
- Chern-Simons invariant
\(S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])\)
Let \(A=(a_1dx+A_1 dt)\otimes X_1 +(a_2dx+A_2dt)\otimes X_2\) be a vector valued form
\(A\wedge A =(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\)
\([A,A]=2(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\)
http://library.wolfram.com/infocenter/MathSource/683/[1]
chapter 8 of http://www.cis.upenn.edu/~cis610/diffgeom-n.pdf
Integrable Hamiltonian hierarchies: spectral and geometric methods http://books.google.com/books?id=uoWMwhA4UNkC&pg=PA466&lpg=PA466&dq=commutator+vector+valued+forms&source=bl&ots=BAl_WcubCU&sig=Hn05qnd8ahVchDY3U3uOerMQ4kY&hl=ko&ei=ZYefTdWnN4fbiALArfyCAw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDsQ6AEwBA#v=onepage&q=commutator%20vector%20valued%20forms&f=false
http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms
history
encyclopedia==
- http://en.wikipedia.org/wiki/Vector-valued_form
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
articles==
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/questions/5962/some-questions-about-differential-forms
- http://math.stackexchange.com/questions/3194/taking-trace-of-vector-valued-differential-forms
- http://mathoverflow.net/questions/31905/some-basic-questions-about-chern-simons-theory
- http://mathoverflow.net/questions/12248/gauge-connections-and-lie-algebras
- http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/questions/5962/some-questions-about-differential-forms
- http://math.stackexchange.com/questions/3194/taking-trace-of-vector-valued-differential-forms
- http://mathoverflow.net/questions/31905/some-basic-questions-about-chern-simons-theory
- http://mathoverflow.net/questions/12248/gauge-connections-and-lie-algebras
- http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field