Chern-Simons Forms appears in several places in physics for examples,

  • Fractional Quantum Hall Effect,

  • response of Topological Insulator,

  • invariant of knot,

  • electromagnetism in 2+1 space-time, and so on.

I need to know about:

  • endomorphism bundle.

  • endomorphism bundle valued forms.

  • exterior covariant derivatives of endomorphism bundle valued forms.

  • trace of endomorphism bundle valued $p$-forms.

  • wedge product of endomorphism bundle-valued p-forms and endomorphism bundle-valued $q$-forms.

  • exterior derivative of Chern-Simons form.

  • exterior covariant derivative of endomorphism bundle-valued $p$-forms.

I am also looking for a book in which required mathematics for working with Chern-Simons forms are discussed. Is there a book in which at least on section was devoted to my questions?

  • In Knot and Physics by Kauffman, I can not find exterior covariant derivative of endomorphism bundle valued forms, trace of endomorphism bundle valued forms, and so on. This book is about Reidemeister moves, writhe number, and so on.

  • In Geometry, Topology and Physics by Nakahara Chapter 10, I can only find exterior covariant derivative of bundle-valued p-forms (vertor valued p-form). How can I work with endomorphism bundle valued p-forms?

  • I have problems with Gauge Fields, Knots, and Gravity by Baez and Mouniani. I think more than 50 present of concepts in this book were left as exercises for reader. Unfortunately all my questions were left as exercises in this book.

  • In mathematical book like Differential Forms and Connections by Darling, my questions were left as an exercise in p. 210.

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/53356/2451 and links therein. $\endgroup$ – Qmechanic Jun 23 '13 at 16:15
  • $\begingroup$ I don't think these book reference requesting questions are still on-topic for this site. $\endgroup$ – Abhimanyu Pallavi Sudhir Jun 23 '13 at 16:20
  • $\begingroup$ @dimansion10 there was never a community agreement to make such questions, often about quite high level advanced topics, off topic ... :-/. It just started to get enforced with zero tolerance since this year. So if you know an answer you have to be fast, even though I think it is important for students and researchers who want to learn a new topic to be able to ask such questions and get good answers from peoplebalready working on the field. $\endgroup$ – Dilaton Jun 23 '13 at 16:41
  • $\begingroup$ @Dilaton: Yes, I quite agree that such questions should be allowed, but I was just informing the OP that his post may get closed so he better be prepared : ) $\endgroup$ – Abhimanyu Pallavi Sudhir Jun 24 '13 at 9:47
  • 1
    $\begingroup$ @Dilaton: This question would likely get closed on MathOverflow. They don't take kindly there to students who can't be bothered to do the exercises. $\endgroup$ – user1504 Jun 24 '13 at 21:02

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