"Vector valued differential forms"의 두 판 사이의 차이
| 19번째 줄: | 19번째 줄: | ||
http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action | 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 ] | |
| − | |||
| − | |||
| − | |||
| − | http://library.wolfram.com/infocenter/MathSource/683/ | ||
| − | |||
| − | http://en.wikipedia.org/wiki/Vector-valued_form | ||
2011년 10월 11일 (화) 05:26 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/[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/
- 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
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field