"Vector valued differential forms"의 두 판 사이의 차이
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<math>[A,A]=2(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]</math> | <math>[A,A]=2(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]</math> | ||
| − | + | http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action | |
| − | + | <br> | |
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| − | + | http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms | |
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<h5>related items</h5> | <h5>related items</h5> | ||
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| + | * [[Knizhnik–Zamolodchikov equations(KZ equations)]] | ||
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* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
* 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 | ||
2011년 4월 13일 (수) 05:02 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://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action
http://library.wolfram.com/infocenter/MathSource/683/
http://en.wikipedia.org/wiki/Vector-valued_form
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
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question and answers(Math Overflow)
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- 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
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