"Vector valued differential forms"의 두 판 사이의 차이

2013년 4월 29일 (월) 06:07 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 \[A\wedge A =(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\] \[[A,A]=2(a_1A_2-a_2A_1)dx\wedge dt \otimes [X_1, X_2]\]

history

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

related items

Knizhnik–Zamolodchikov equations(KZ equations)

encyclopedia

http://en.wikipedia.org/wiki/Vector-valued_form

question and answers(Math Overflow)

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
 ==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]]
+:<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>
 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>
-<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://library.wolfram.com/infocenter/MathSource/683/
+* http://en.wikipedia.org/wiki/Vector-valued_form
+* chapter 8 of [http://www.cis.upenn.edu/%7Ecis610/diffgeom-n.pdf 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://library.wolfram.com/infocenter/MathSource/683/[http://en.wikipedia.org/wiki/Vector-valued_form ]
+* http://math.stackexchange.com/questions/3192/gauge-transformations-in-differential-forms
-chapter 8 of [http://www.cis.upenn.edu/%7Ecis610/diffgeom-n.pdf 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==
@@ 43번째 줄: / 29번째 줄: @@
 * http://www.google.com/search?hl=en&tbs=tl:1&q=
 ==related items==
@@ 51번째 줄: / 37번째 줄: @@
 * [[Knizhnik–Zamolodchikov equations(KZ equations)]]
 ==encyclopedia==
 * http://en.wikipedia.org/wiki/Vector-valued_form
-* 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]])
-==books==
-* [[2011년 books and articles]]
-* http://library.nu/search?q=
-* http://library.nu/search?q=
-==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/%7Ereb/papers/index.html 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<br>
+* http://mathoverflow.net/questions/36178/what-is-the-trace-in-the-chern-simons-action
-==blogs==
-*  구글 블로그 검색<br>
-**  http://blogsearch.google.com/blogsearch?q=<br>
-** http://blogsearch.google.com/blogsearch?q=
-* http://ncatlab.org/nlab/show/HomePage
-==experts on the field==
-* http://arxiv.org/
-==links==
-* [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/
 [[분류:개인노트]]
 [[분류:math and physics]]