"Vector valued differential forms"의 두 판 사이의 차이

2011년 4월 13일 (수) 04:56 판

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

\(A\wedge A =(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\)

\([A,A]=2(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\)

[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

[3]http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms

introduction

history

http://www.google.com/search?hl=en&tbs=tl:1&q=

related items

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

question and answers(Math Overflow)

blogs

구글 블로그 검색
- http://blogsearch.google.com/blogsearch?q=
- http://blogsearch.google.com/blogsearch?q=
http://ncatlab.org/nlab/show/HomePage

experts on the field

http://arxiv.org/

@@ 3번째 줄: / 3번째 줄: @@
 http://math.stackexchange.com/questions/3194/taking-trace-of-vector-valued-differential-forms
-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://mathoverflow.net/questions/31905/some-basic-questions-about-chern-simons-theory
@@ 15번째 줄: / 15번째 줄: @@
 <h5>exercise from Chern-Simons theory</h5>
-<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>
+* [[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>
+Let <math>A=(a_1dx+A_1 dt)\otimes X_1 +(a_2dx+A_2dt)\otimes  X_2</math> be a vector valued form
+<math>A\wedge A =(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 ]http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action
@@ 35번째 줄: / 45번째 줄: @@
-http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms
+[http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms ]http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms
+<h5>introduction</h5>
+<h5>history</h5>
+* http://www.google.com/search?hl=en&tbs=tl:1&q=
+<h5>related items</h5>
+<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>
+* http://en.wikipedia.org/wiki/
+* http://www.scholarpedia.org/
+* [http://eom.springer.de/ http://eom.springer.de]
+* http://www.proofwiki.org/wiki/
+* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
+<h5>books</h5>
+* [[2011년 books and articles]]
+* http://library.nu/search?q=
+* http://library.nu/search?q=
+<h5>expositions</h5>
+<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>
+* 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/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
+* http://dx.doi.org/
+<h5>question and answers(Math Overflow)</h5>
+* http://mathoverflow.net/search?q=
+* http://mathoverflow.net/search?q=
+<h5>blogs</h5>
+*  구글 블로그 검색<br>
+**  http://blogsearch.google.com/blogsearch?q=<br>
+** http://blogsearch.google.com/blogsearch?q=
+* http://ncatlab.org/nlab/show/HomePage
+<h5>experts on the field</h5>
+* http://arxiv.org/
+<h5>links</h5>
+* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
+* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
+* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
+* http://functions.wolfram.com/