Vector valued differential forms

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/36178/what-is-the-trace-in-the-chern-simons-action

http://mathoverflow.net/questions/31905/some-basic-questions-about-chern-simons-theory

http://mathoverflow.net/questions/12248/gauge-connections-and-lie-algebras

 

 

exercise from Chern-Simons theory

\(S=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{2}{3}A\wedge A\wedge A)=\frac{k}{4\pi}\int_M \text{tr}\,(A\wedge dA+\tfrac{1}{3}A\wedge [A,A])\)

 

 

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