Talk:Classical field theory

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Can someone do the derivation of interesting conserved quantities in EM? GR source equations and lagrangian

Contents 1 Edits on 22/12/05 2 Relativistic invariance 3 Name change? 4 Article name is fine; major cleanup needed though 5 Some questions 6 Recent edits

[edit] Edits on 22/12/05

I have begun performing several edits, and have forgotten to comment the edits. The initial few edits were adding relativistic invariance. Apologies for any inconvenience caused. Masud 15:32, 22 December 2005 (UTC)

I have added relevant sections. They still need touching up, which I may do later, and I have yet to add the source lagrangian for the EM field and general relativity. Masud 16:23, 22 December 2005 (UTC)

[edit] Relativistic invariance

Does this section in the article belong in the SR article? Or perhaps another article altogether. Masud 16:23, 22 December 2005 (UTC)

There is a Spacetime physics section in the SR article...maybe this should have a link to that? Masud 13:02, 24 December 2005 (UTC)

[edit] Name change?

Perhaps a better title for this article might be "Lagrangian formulation of electrodynamics". In fact, I'd strongly recommend that change. linas 16:37, 24 December 2005 (UTC)

But the page has information on general classical fields. I can then add a GR section too. And if we did rename it, we'd lose a page on classical fields in general, which I think is as necessary as the (much higher profile) quantum field theory page. Masud 16:42, 24 December 2005 (UTC)

You are new to WP, so allow me to make some suggestions and pointers. First, WP is not a book, and shouldn't be written as if it were one. The article is already fairly long, and it deals with just one topic (electromagnetism). Adding GR would only make it longer. Thus, I would suggest that you write two articles; a second on the lagrangian formulation of GR.

Next, you are currently rather far form an article on "classical fields" in general. First, the article assumes four space-time dimensions. That is a strange limitation. Next, there are a vast number of possible lagrangians; focusing on E&M or GR may have physical importance, but cuts out oceans of other interesting things. Also, note that the modern mathematical understanding of E&M is as a line bundle over U(1). The pdf Line Bundles by Micheal Murray provides an excellent overview of electrodynamics in this context, and you might do well to study that.

Based on these remarks, I suggest that you try to narrow your focus to something more humble, a limited-scope, single-topic article, something for which you do have a good grasp, rather than attempting an over-arching, reviews-all-human-knowledge type of an article. (I note that Landau and Lifshitz, "the Classical Theory of Fields", is hundreds of pages long, and dense to boot. Each section of that book might make an appropriate WP article: that would result in 50 or 100 of articles.)

BTW, you may enjoy following the conversations at Wikipedia:WikiProject Physics, where various general topics are discussed. linas 17:07, 24 December 2005 (UTC)

That's actually quite patronising. I've been a member of Wikipedia longer than you, and have been editing before that. Masud 09:48, 26 December 2005 (UTC)

I'm sorry, based on your edit history, it seems that you've been here a few weeks. I've been here for almost a year. linas 20:33, 3 January 2006 (UTC)

Apology accepted; but just for the record, my edit history starts from 5 July 2004, and your earliest edit is 30 December 2004. Masud 02:45, 4 January 2006 (UTC)

[edit] Article name is fine; major cleanup needed though

I'm with Masud on the issue of the article containing more than just a description of one field theory. The article is called 'classical field theory' and this includes more than just any particluar field theory - EM, GR etc. and Newtonian gravitation; yes, that's right, Newtonian gravitation is a classical field theory. Which brings me to another point: classical field theories are not necessarily Lorentz covariant as the article claims (and incorrectly gives the example of the string). Depending on how much information we want to include on each classical field theory, other articles on EM, GR etc. may be needed. MP (talk) 09:57, 3 January 2006 (UTC)

I agree with you on the cleanup. Am attempting to separate relativistic and non-relativistic fields. Note that the electric field (also initially treated non-relativistically) was the first field recognised as a field, then the gravitational field was described in the same way. Then came magnetic fields, etc. Masud 15:13, 3 January 2006 (UTC)

Have tried to add some to the non-rel. grav. field. I'm not sure if I like the arrow-on-top or heavy type notation for vectors. Is there a Wikipedia convention for which one to use? Masud 15:40, 3 January 2006 (UTC)

I'm still concerned about the scope. Classical fields include sound-waves/acoustics in air, ocean, and earth (geophysics). Classical fields also include wind fields, humidity fields, pressure fields, etc. for predicting weather. Then, in supernova research, one solves classical field equations for a detonation front (supersonic burning) (of nuclear material, biut that's besides the point). Note that in burning, the number of particles are not constant. (Ditto for rainfail). One also has lots and lots of clasical fields in KdV and fluid dynamics and turbulence and etc. One uses classical (albeit fractal) fields to model the stresses in a sheet of metal, thus leading to the propagation of stress fractures in solids (which are fractal). Speaking of fractals and classical fields: DLA diffusion-limited aggregation. Then, the diffusion-reaction equation. and etc. By focusing on E&M and gravity, this article is ... very very incomplete. linas 20:29, 3 January 2006 (UTC)

You make a very good point. But clearly we are attempting an article on fundamental classical fields. I also note that the article on QFT does not have sections on every imaginable quantum field either. People who know about and are looking for propagation of stress fractures in solids would probably look that up independently as opposed to coming to this page to find it; besides assuming someone has written this content, we could easily have short paragraphs and subsections which link to these pages. Masud 02:53, 4 January 2006 (UTC)

I beg to differ. The article on QFT makes an attempt, in the introduction, and then in the body, to actually list every possible QFT. Its misses a few of the minor ones but after a quick skim, seemed to touch all the major ones. I'd also like to point out that the QFT article is a rather poor role model for what a WP article should look like; its in pretty nasty condition, and poorly structured. It has all the symptoms of an ambitious editor who couldn't/didn't finish the job that was started.

The comment about stress fractures reinforces my point, instead of weakening it. The reader of an article on weather prediction, or somesuch, does indeed start there, not here. On reading, they realize that they now have a general question about the theory of continuous media, and would thus hopefully be linked here. They come here, and rather than learning about the classical theory of fields, they see nothing but a sea of gravity and electromagnetism.

I'll say it a third time, and then I'll grit my teeth: either write the general survey article that the title promises this to be, or change the title to reflect its actual contents (which currently is rather narrow, a mix of "the classical theory of electromagnetic fields in a vacuum with no boundary conditions", and some newtonian gravity, which, honestly, to me, are rather unrelated.) Honestly; I'm not trying to be offensive; I'm trying to be helpful: you'll have a better article if you narrow the scope. linas 05:14, 4 January 2006 (UTC)

The term 'classical field theory' is most commonly used for things like electromagnetism and GR and the article should certainly discuss these. Having said that, Linas' point about including other fields (humidity, pressure etc.) can't be ignored. I think a compromise is in order here. Be aware, however, that when a physicist comes across a 'classical field theory' nowadays, they also come across Lagrangians and this point should be emphasised when discussing more up to date classical field theories. This article should have links going to the other less well-known classical fields, but a big deal should not be made of them here (for example, I don't believe meteorologists - or anyone for that matter - ever use Lagrangians to determine how a test particle moves in a wind field). Let's keep things in perspective. MP (talk) 08:17, 4 January 2006 (UTC)

[edit] Some questions

See the to-do box, I've duplicated here for convenience and permanence.

Question: do we derive the field equations given the Lagrangians? Or do we delegate that to some other article? (eg. GR's field equations derivations are presented in other pages on Wikipedia).

Question: do we include more details on the non-relativistic fields? Those sections are looking quite thin at the moment.

Masud 14:20, 15 January 2006 (UTC)

Hi Masud. Good questions; I propose that we don't derive the field equations in this article (as this would be too much detail for this article and) as the equations for GR are derived in Einstein-Hilbert action. However, the Lagrangians, field equations and conservation laws should be mentioned (as they're obviously worthy of mention). It may even be too much to mention all the different Lagrangians and field equations for one classical field theory - vacuum and non-Einstein vacuum equations (and similarly for EM). Perhaps we could state the most general Lagrangian for each theory and just briefly mention the vacuum cases).

[edit] Recent edits

I've edited the EM section to include source terms in the equations, re-organised the headers, and feel that the tags are not required as much anymore.

I'm not sure if it would be a good idea to add the magnetic field as a non-relativistic field theory. Anyone have any thoughts on the matter? Masud 02:05, 14 February 2006 (UTC)