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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.

Dilaton
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Sobouti
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  • Possible duplicates: http://physics.stackexchange.com/q/53356/2451 and links therein. – Qmechanic Jun 23 '13 at 16:15
  • I don't think these book reference requesting questions are still on-topic for this site. – Abhimanyu Pallavi Sudhir Jun 23 '13 at 16:20
  • @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. – Dilaton Jun 23 '13 at 16:41
  • @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 : ) – Abhimanyu Pallavi Sudhir Jun 24 '13 at 09:47
  • @dimension10 I see, and note that it is not stack exchange that disallows even the good and well defined enough ones as Shog9 said, but some people here. When you read through the corresponding meta discussions you can see that there are good people who post good stuff on the main page who say it should be alloed. If enough people with 3000 rep think like this the good ones could be made allowed again, as it has been the case before the elections, since 5 people can reopen posts for example ... – Dilaton Jun 24 '13 at 11:01
  • With this specific question it might be not that bad that it is closed, since maybe the OP can find what he needs in the other question. However, I disagree that the two questions are exact duplicates, since asking about Chern- Simons forms is much more specific than about topological field theory generally. – Dilaton Jun 24 '13 at 11:22
  • @Manishearth, can this be reopend since it is not a duplicate and the OP says the answer in the other question, as well as some sources he has serached himself do not cover what he asks about? – Dilaton Jun 24 '13 at 20:29
  • @Sobouti if your question does not get reopend even though it is not a duplicate and much more specific than the linked to question, you could try to ask it on Math, or probably even better since it is very high level on MathOverflow. Of I only could I would vote to reopen ... – Dilaton Jun 24 '13 at 20:36
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    @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. – user1504 Jun 24 '13 at 21:02
  • @user1504 does the exercise mentioned in the last bullet point really exactly ask about what is in the title of this question? If so the book should have explained these things in the text before posing such an exercise... To me this looks like a rather good enough and interesting question at least for Physics SE. And it is definitively not isomorphic to generally asking about topological field theory. – Dilaton Jun 24 '13 at 21:10
  • Aah @Qmechanic has reopend :-). I just hope none of the other mods will overrule him, as I have already seen it happen (and this should definitively not happen since he is the one with the deepest and broadest physics knowledge, his word and activities should be respected) – Dilaton Jun 24 '13 at 21:16
  • Darn, can people now leave this question alone? Qmechanic has just reopend it and if he thinks it is good enough than it is! Why does it need to have a closevote again? Asking about the use of this concepts in Chern-Simons theory is a perfectly good and valid high level question. – Dilaton Jun 26 '13 at 12:04
  • Here are some answers for Part 2 of Baez´s book. http://www.ugcs.net/~yukon/docs/gfkg-II.pdf – aortizmena Jul 09 '13 at 02:24

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