Talk:Classification of electromagnetic fields

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[edit] Classification problem

Introduced the classification problem. Now for the juicy stuff ... --Mpatel 09:29, 27 July 2005 (UTC)

Hi, MP, did you ever come back to write the "juicy stuff" for this article? I'm guessing you didn't, since the promised connection between the classification of bivectors and the classification of EM fields has not been established, and the physical meaning of electrostatic, magnetostatic has not been discussed (see Landau and Lifshitz).

I think the first half of this article should be split off to form part of an article on bivectors (if there already is one, it must need a lot of work if it doesn't already discuss the classification!), which should be in suitable math categories and should link to relevant articles in algebraic geometry (e.g. Grassmannians use bivectors and even p-vectors) as well as to an article on EM fields. Maybe the material on the EM field in this article should also be moved, to form part of an article on "Relativistic formalisms for electromagnetism"? Someone we need to make it easy for students to effortlessly learn all the most useful stuff. For example, isotropy groups of null versus non-null are not even mentioned in this article! But it is essential to understand why null EM fields have one more symmetry!

After fixing up all these problems, in the next round, more can be done, once we have good articles on tangent spaces and so forth. At present, the stuff about thinking about Minkowski space as a Lorentzian manifold versus thinking about it as real inner product space will be very confusing to students, but they need to understand this in order to understand how the equivalence principle is elegantly incorporated into the geometric formalism simply by assuming that spacetime is a Lorentzian manifold, so that its tangent spaces are all isomorphic to E^1,3.

I tried to improve the article, but got tired before I really finished, so I think this still needs substantial work in terms of improved exposition, giving more information in less space, etc. Hope this is helpful; I might sound a bit cranky since things seem to be going so slowly---CH (talk) 06:24, 18 August 2005 (UTC)

P.S. I didn't finish my thought: I am trying to suggest that this material should be ported/developed into more detailed discussion in two different articles:

1. bivectors, discussing material hinted at here, including
   • classification, with examples of null, non-null
   • differential forms and bivectors
   • special caes of "simple" p-vectors in Grassmannians
2. Relativistic formalisms for electromagnetism, including how Hodge dual, bivectors, Mawell equations, etc., are treated using
   • vector calculus on euclidean space
   • index gymnastics on Minkowski space (with generalization to any Lorenztian manifold)
   • differential forms

Hope this gives the idea---CH (talk) 06:37, 18 August 2005 (UTC)

P.P.S. I guess I still didn't finish my thought: a general strategy which possibly should be implemented consistently is to carefully separate all the algebraic stuff holding in tangent spaces (which often has beautiful connections with algebraic geometry, stuff which increasingly physicists need to know) from stuff which follows easily via general category theory abstract nonsense from "bundling" vector spaces into tangent bundle, jet spaces, tensor bundles, whatever. In other words, rigorously split discussion of vectors, linear operators, multilinear operators (tensors), frames, etc., from smooth sections of the corresponding bundles, which are vector fields, tensor fields, frame fields, etc. Note that "frames" are simply the Lorentzian inner product take on the euclidean frames used to form Stiefel manifolds in mathematics, etc. Hope this makes sense---CH (talk) 06:46, 18 August 2005 (UTC)

P.P.P.S. Hope these postscripts will come to an end soon, gosh. I signed you and EMS up for WikiProject GR; I am still drafting the manifesto (I will have to revisit all these talk pages and try to organize all the suggestions I have made into coherent themes, which will be time consuming). Anyway, one key point to be made in the manifesto is that all serious Wikipedia articles should include at least one really appropriate citation to a good textbook, and perhaps more. I stress that I don't envision turning every Wiki article into a review article. Rather, good Wiki articles should guide curious readers to such reviews (or to textbooks), and should help him to understand what he reads and to tie it all together.---CH (talk) 06:50, 18 August 2005 (UTC)

Hi CH. It seems like I never did get back to writing the 'juicy stuff' - I remember you mentioned some references, but I don't have them and couldn't get a hold of them. I also got distracted by other articles. I would need a bit of time to check out some of the details of your superior plans for this article. It seems as though your plans for this article are far more ambitious than mine. You can go ahead and improve this article in any way you see fit. ---Mpatel (talk) 15:53, August 18, 2005 (UTC)

[edit] Students beware

I had been monitoring this article, but I am leaving the WP and am now abandoning it to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions.

Good luck in your seach for information, regardless!---CH 23:03, 30 June 2006 (UTC)