Talk:Gauge covariant derivative

message: Isn't it so that the gauge covariant derivative and the covariant derivative of GR are a partition of the mathematical covariant derivative. In GR the vector bundle is the tangent bundle and the gauge group is GL(4, R), which could be reduced to SO(3, 1). The gauge cov. der. is for all vector bundles which are not the tangent bundle. Right? --MarSch 10:50, 21 October 2005 (UTC)
replies: text: The term covariant derivative is often used to describe connections on other vector bundles as well.  However, this is not the agreed upon usage for Wikipedia because covariant derivative has a very precise meaning in physics.  Instead, the intrinsic description of a "gauge" covariant derivative can be found in the article Koszul connection (which is fairly standard nomenclature between mathematicians and physicists).  Silly rabbit 15:48, 27 June 2006 (UTC)
thread_title: Relation to other derives

message: Someone reverted my recent edits but did not care to explain why they thought they were revert-worthy.  Perhaps here, on the talk page, would be a good place to have such a discussion?  I'm not sure what the objection could possibly be, so let me explain how I came to write the long intro section. I'd just reviewed and made minor corrections to other related articles, e.g. vertical bundle and exterior covariant derivative. Then I stumbled onto this article.
There are already several nice articles on WP on the guage covariant derivative, but this one stood out as (1) being the very simplest, least complicated of the set, and (2) it completely failed to explain what was going on.  The first sentence was even wrong. 
So, my first edit was to point out that he gauge covariant derivative is exactly the same thing as the exterior covariant derivative.  Then I realized that perhaps this was too obtuse a statement, the kind where everyone accuses WP of being too abstract and too incomprehensible and too hard to understand. So then I thought I should simplify the statement. After simplifying it, I compared it to the rest of the article, and it was clear that even then, all of the other affine connection articles on WP were far more abstract and complex, as compared to this one. This article deals with the simplest-of-the-simple introductions to the connection.  So I thought, rather than glomming it up with lots of complex equations, I thought it would be best to keep it very simple, and keep it accessible to young students.  Thus the intro: it points out that there are more abstract, more beautiful approaches to the topic, but keeps the rest of this particular article very low-brow, very simple.  Which seems like a good idea -- there needs to be someplace to start learning this stuff.
Is that a good enough explanation for what this is all about?  67.198.37.16 (talk) 02:08, 24 April 2016 (UTC)
replies: text: See, for example, the "Request" discussion immediately above. It would be a very worthy project to create a "rosetta stone" that translates the notation used here to the standard notation used by mathematicians. I have not yet stumbled on any other article on WP that makes this "connection".  It would be good to have, and this article might be an OK place for that. 67.198.37.16 (talk) 02:30, 24 April 2016 (UTC)
replies: text: Original synthesis?  This is standard textbook material commonly taught in physics grad-school classes. See for example David Bleeker, "Gauge theory and variational principles." (1982) Or Misner, Thorne, Wheeler (1972) -- or lectures from I.M. Singer in the 1970's. There are surely many other books. If your professors are not at least mentioning this material in class, you should probably be looking around for better professors.  This may seem like a combative statement, but seriously, if you think that this is "original synthesis", you really need to schedule some office time with your prof, and start asking questions about differential geometry. If he stalls, you need to escalate to the dean.  You should not in any way have the impression that something new is being invented here:  this book review sketches out the history, back to the 1930's, Hermann Weyl and Einstein himself, and the recognition of these ideas in the late 1950's, developement in the 1960's and the solidification and maturation of these ideas in the 1970's. It is the duty of your professors to teach you at least some of the basics of this stuff. 67.198.37.16 (talk) 16:04, 24 April 2016 (UTC)

text:  Here, the bleeker book is so so old that its online as a PDF  Its not a great book, because although its quite accurate, it fails to provide insightful commentary.  But see for example, page 26 for the PFB, page 29 for the connection page 30 for the fundamental field, page 33 for the gauge potentials and electromagnetic field strength, chapter 3 for particle fields, page 43 for particle fields living in the associated bundle and hopping ahead .. chapter 6 for the Dirac fields, and page 81ff for spin structures and the Dirac eqn. 67.198.37.16 (talk) 16:15, 24 April 2016 (UTC)
replies: text:  Here, I'll just add these as refs to the main article.  This article reads like an orphan raised by wolves; civilizing it is more work than I care to put in, but it certainly does need lots of loving care from someone. 67.198.37.16 (talk) 16:24, 24 April 2016 (UTC)
thread_title:  Some need for some discussion 

message: I fixed this: "The gauge fields here belong to the fundamental representations of the electroweak Lie group U(1)⊗SU(2) times the color symmetry Lie group SU(3)" but someone reverted it back. Well. Check just about any other article (e.g gluon field) or any QFT book. Gauge boson fields are in adjoint rep. Fundamental reps of SU(n) are n-dimensional, while adjoint reps are (n^2-1)-dimensional. Now, how many gluons are there, 3 or 8?
213.175.37.10 (talk) 12:49, 20 December 2017 (UTC)
replies: text: You are correct. JRSpriggs (talk) 20:30, 2 January 2023 (UTC)
thread_title:  Gauge fields belong to _adjoint_ reps