Talk:Lorentz group/Archive

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Contents

ToDo

To do: add section on Lie algebra, and one on representations of the Lorentz group. Discuss relationship of the Lorentz group to special and general relativity. -- Fropuff 16:45, 11 Feb 2004 (UTC)

Connectedness

It is a 6-dimensional noncompact Lie group which is neither connected, nor simply connected.

Can something be simply connected without being connected? Josh Cherry 04:44, 18 Nov 2004 (UTC)

Technically speaking, no. What is meant is that the connected components of the Lorentz group are themselves not simply connected. We could say this instead but it's a little more wordy. -- Fropuff 06:21, 2004 Nov 18 (UTC)

I've changed this. Maybe it's just me, but what was there left me scratching my head, much as though someone had said this number is neither an integer, nor an even integer. Josh Cherry 23:54, 18 Nov 2004 (UTC)

Elaboration in Progress

Hi all, I added a bunch of improvements to this article yesterday, but unfortunately the server lost all my work! I am trying again today.

I plan to

  • improve the introduction, placing the Lorentz group and restricted Lorentz group in a clearer context mathematically and physically,
  • add section on conjugacy classes (maybe eventually adding some illustrations of the flow lines typical of elliptical, hyperbolic, parabolic, and loxodromic one-parameter subgroups),
  • add section on the Lie algebra, giving two nice generating sets,
  • add section on appearance of the night sky, explaining the isomorphism between restricted Lorentz group and Moebius group, and its physical consequences,
  • add section on subalgebras of the Lie algebra, eventually adding a lattice diagram showing their relations, and discussing some of the more important homogeneous spaces (coset spaces) and their physical signficance.

Because of the close connection with Möbius transformations, I plan to also improve the article on Möbius transformations, putting the more mathematical material in the latter article, and putting more of the physical interpreation in this one.

At present, Wikipedia lacks a suitable discussion of

  • bivectors
  • point symmetry group of an (ordinary or partial) differential equation, or system of same

Eventually, I hope to repair this gap by writing new articles and revising more old ones as appropriate.---CH (talk) 2 July 2005 22:09 (UTC)

OK, I've pretty much carried out the above plans. I still need to add a figure showing the lattice of subalgebras (up to conjugacy).

I also need to create figures showing the flow lines of parabolic, elliptic, hyperbolic, and loxodromic flow lines. I think I see how to create .png images, but does anyone know how to create an animated picture which can be used on Wiki, say using Maple? Are anitmated .gif images acceptable?--CH (talk) 3 July 2005 04:05 (UTC)

Misc statements

Article states:

...For example, it arises as the point symmetry group of a certain ordinary differential equation...

Perchance the diff eq you are looking for is the Picard-Fuchs equation? or are you looking for the hypergeometric differential equation? By point symmetry group, do you mean the monodromy group? The Mobius transforms are the monodromy group of this differential equation.

In pure mathematics, the restricted Lorentz group arises as the Möbius group, which is the symmetry group of conformal geometry on the Riemann sphere. In even more sophisticated language, it is the group of holomorphisms of the complex projective line.

I think this is incorrect, I think its not the group of holomorphisms but the monodromy action which are the Mobius transforms. I started to try to write this up in Riemann's differential equation, (scroll to the bottom, fractional linear transformations), and the cluster of related articles (e.g.the bottom of the article hypergeometric differential equation), but got distracted. I mean to come back later and finish this. -- linas 3 July 2005 18:11 (UTC)

Hi, Linas. If the pun was intentional, I wouldn't say those were misstatements. It's a terrible gap that there is nothing in Wikipedia yet on point symmetries of differential equations, but bye and bye I'll try to supply the gap and then everything I said will become clear. I meant the fundamental invariant of the Lorentz group. (See the books by Peter J. Olver). Right now I am not sure about the relation (if any) with monodromy. Information about geometric invariant theory wrt Lorentz seems hard to come by (or else I am not looking in the right place). As for holomorphisms, at that point in the article, I struggled somewhat for words to express clearly and concisely what Penrose said about this, because appropriate articles to link to are not yet available in Wikipedia. Penrose's claim is that the Riemann sphere can be viewed as an analytic complex closed curve, and then the Möbius group is the group of self transformations preserving this structure. These are usually called holomorphisms, agreed? But if you still think what I said is misleading, I can just remove that sentence (probably best to let me do the edits right now to avoid that nasty edit conflict problem) --CH (talk) 3 July 2005 19:29 (UTC)
OK. Well, I was just trying to point out that the links that I think you are fishing for were appearing in the the articles on the hypergeometric equation, wherein I was starting to describe the symmetries of the Riemann sphere. I have not heard of the fundamental invariant of the Lorentz group (I have not heard of a lot of things). Are you looking for invariant theory or invariant polynomial? . linas 6 July 2005 01:35 (UTC)
The only use of point symmetry group that I know of in physics is that of crystallographic point group; is that the link you are looking for? For general Lie groups, we have the article lattice (group), which is not very deep. But if you are thinking specifically in terms of SL(2,C), we have the articles Fuchsian group and Fuchsian model. We also have articles on fundamental region, which is a kind of generalization of the Brillouin zone to general Lie groups; the picture illustrates the fundamental region for SL(2,Z). I'm planning on writing an article on the Dirichlet polygon real soon now; we already have fundamental polygon. But these are not directly relevant to the Riemann sphere; the sphere is very special. The only other directly relevant point-symmetry link I can think of is the fact that the Riemann sphere can be tiled with triangles; all of which are special cases of triangle groups. These show up as the Schwarz maps in the theory of hypergeometric functions, which are those mappings of the Riemann sphere that are described by SL(2,C). So when you say "holomorphic mappings of Riemann sphere", the only related topic that pops into mind is "hypergeometric function". But this is all very very far from where most physicists live and think when faced with the Lorentz group. I once read chapter 1 and 2 of Penrose's twistor theory book, I'm pretty sure he didn't mention any of the above topics. However, I'm told that string theory has breathed new life into twistor theory, I've heard that even Ed Witten himself said so, so maybe this is what physicists think about these days :-/ linas 6 July 2005 03:20 (UTC)
Another "fundamental" thingy that is SL(2,C)-related is the j-invariant of elliptic curves. Another sl(2,whatever) algebra topic with the word "fundamental" in it are the fundamental Weyl chambers of Lie groups. Finally, there is something called a relative invariant, which is a polynomial that transforms as the character of a group element. The ratio of these again are Schwarz maps or something like that; I'm not clear on this. I'm only learning this stuff now. linas 6 July 2005 03:41 (UTC)
As far as I know, we have close to nothing about point symmetries of differential equations in Wikipedia. There is something at Noether's theorem, but that article is, uhm, not the best we have. I hope somebody will be able to fill this gap sometime. -- Jitse Niesen (talk) 12:58, 10 July 2005 (UTC)
Linas, Jitse is correct. Point symmetry groups in the sense of Lie's theory of symmetry of differential equations are a completely different concept from the isotropy groups of crystallographic groups, and despite their huge importance both for theory and applications, as far as I know there is so far nothing about them in Wikipedia. (But crystallographic groups are related to root lattices, which are related to the Coxeter groups which came up in the Baez posts I tried to point you at. And Coxeter groups involve Dynkin diagrams, and from E. B. Dynkin I learned about the Möbius group, in a course on complex variables. And the editor who once chided me for a late report regarding an article related to crystallographic groups was H. S. M. Coxeter. No wonder mathematicians are paranoid. But could you please trust me on this anyway?)
Re monodromy, see the book by Jones and Singerman. (I already tried to point you at Baez's more recent posts on modular forms.) Ultimately, everything is related, and mathematics forms an organic whole, but you may need to restrain your enthusiasm just long enough to learn what people really mean by topic X before you try to connect X to Y.
Since you, Linas, seem to be fighting tooth and nail, I am removing the offending reference to complex closed curve until I can write the articles which clarify this. It's gratifying in a way that you are impatient to learn what I'm talking about--- see for example the book Applications of Lie Groups to Differential Equations by Peter J. Olver. In general, I know you're trying to help, but when I mention a term I try to look for existing links, and I don't agree that the articles you mentioned explain the connections I have in mind, OK?---CH (talk) 01:36, 11 July 2005 (UTC)

Representations and Invariants

Hmm... I seem to already be over the recommended size limit, but haven't even mentioned the irreps or invariants. (These are important in physics as well as math, so there is a case that they should be mentioned in this article.) I think there should be at least short sections briefly indicating at least some of the most basic results. How serious is it that the article seems to be over 30 KB? I'll stop adding more until someone let's me know about this.--CH (talk) 3 July 2005 19:29 (UTC)

It's not serious; the problem is that the article may grow too long to read in one go, which may happen if the article grows over 30 kB (excluding mark-up commands). The usual solution is to split the article up, as Fropuff is suggesting below. You can read a bit more at Wikipedia:Article size and Wikipedia:Summary style. I hope that answers your questions, but whatever you do, don't stop writing; you can always have others worrying about proper organization. -- Jitse Niesen (talk) 13:07, 10 July 2005 (UTC)

Quibbles over Terminology: Complex Closed Curve, Bianchi Group, Kleinian Group

Whoever changed complex closed curve to complex projective line, I don't think you are helping, since existing articles will only confuse readers if they go there from this article. My idea was to leave red links until improved articles can be written. The red links might encourage some of you to write the missing articles! If you disagree, maybe we should discuss this here before you make more apparently minor changes of wording? If you guess wrong about my intentions, you could change a correct statement into an incorrect one--CH (talk) 3 July 2005 19:45 (UTC)

That was me. Sorry; change it back. Since you were talking about symmetries of the sphere, I assumed you meant Riemann sphere aka the complex projective line, and were unaware of the WP article on this. I guess I don't know what a complex closed curve is, then. linas 6 July 2005 01:35 (UTC)

P.S. To mention some specific red links I'd like to leave red for the present: I intend to write articles on Bianchi group (this should even be a category with separate articles for each group) and Kleinian geometry. Someone else can write one on deformation retracts. Can the well intentioned but misleading redirect for complex closed curve be removed? Possibly someone can write a proper article on twistor theory and then this "controversy" can be cleared up by having this article refer to that one.--CH (talk) 3 July 2005 19:51 (UTC)

Re Kleinian geometry, perhaps this should be a redirect to Kleinian model? We also have articles on Kleinian group and hyperbolic 3-manifold; I don't think it makes sense to write a fourth article on what is, (I assume must surely be) more-or-less the same topic; so it seems to me that Kleinian geometry should redirect to one of these three. linas 6 July 2005 01:35 (UTC)
Re Bianchi group, I assume you mean SL(2,O_K) for the ring of integers O_K It seems we do not have any articles on the ring of integers. and the nest of Galois group articles are shallow. We don't have any articles on real places and imaginary places. linas 6 July 2005 15:36 (UTC)
Hi, Linas-- Yes, CP1 is a complex closed curve, but I dislike emphasis of that article. No, Kleinian geometry is a completely different concept from Kleinian group and Kleinian model of Hn, although they are related concepts. For example, Kleinian model is the ball model of Hn, while Poincare model is upper half space model; either way, Hn is an example of a Kleinian geometry. A Kleinian geometry is a homogeneous space, but the emphasis is sufficiently different that the concept deserves an article of its own. As for Bianchi group, this term refers to Bianchi's classification up to Lie group isomorphism of the three dimensional real Lie groups and it is a standard term in both math and physics. SL(2,R) or Bianchi VIII and SO(3) or Bianchi IX are two of the nine classes. The group UT(3) of three by three upper triangular matrices with ones on diagonal is Bianchi II, and so forth. These are beautiful and important examples of Kleinian geometries and they well illustrate the close connections with the ideas of Lie and Klein on symmetry groups, particularly symmetries of differential equations. This is lovely stuff; I can't do it justice here, hope to do a decent job when I find time to write the planned articles---CH (talk) 09:41, 10 July 2005 (UTC)

FYI, be aware that here at UT Austin, the math dept calls SL(2,O_K) the Bianchi group. See [1] and [2] and [3] Perhaps you should call it Bianchi classification? For upper triangular matrices, we have the article Borel subgroup. linas 17:49, 10 July 2005 (UTC)

Huh, never heard that before. If you search gr-qc section of ArXiv, or look in gtr books in library, you will find that "Bianchi groups" (plural) is a standard term to refer to the 9 isomorphism classes in Bianchi's classification. But yeah, it would make sense to call the article Bianchi classification, but because Bianchi group is more common, there should be a disambiguation page. ---CH 19:55, 10 July 2005 (UTC)
Just looked up the definition you have in mind. Linas, your Bianchi groups are generalizations of the modular group PSL(2,Z), which incidentally came up in my dissertation in connection with simple continued fractions. Specifically, Γd = PSL(2,F) where F = Od is the ring of algebraic integers for a quadratic extension of the rational numbers. But my Bianchi groups are, as I said, the nine isomorphism classes of three dimensional real Lie groups, which is clearly a completely different concept.---CH (talk) 01:05, 11 July 2005 (UTC)
P.S. Linas, you would get a kick out of several consecutive This Week in Mathematical Physics articles in which John Baez discussed parabolic subgroups, Coxeter groups, cohomology, and many other things. This might help give you a sense of why subalgebras and Kleinian geometries are important, but even this is only the tip of the iceberg. One thing I'd like to write up in a much more reader-friendly way is the connection between material he discussed and topics in algebraic geometry such as Schubert calculus. Re UT Austin: are you in the math or physics department? Do you know Charles Radin? Speaking of low dimensional Lie groups, he's worked with John Horton Conway on quaquaversal tilings, if you know what those are. He is a tireless proponent of the ergodic theory viewpoint in math---CH (talk) 22:46, 10 July 2005 (UTC)

Split?

This article is getting a little long, even though more needs to be said. Perhaps we should split off the Lie algebra stuff to its own article (e.g Lie algebra of the Lorentz group). We should probably also start an article on representations of the Lorentz group. -- Fropuff 8 July 2005 23:50 (UTC)

Hi, Fropuff, I don't like the first idea at all! I know I raised the issue of length myself, but as I continue to read more and more pages in the Wikipedia, my confidence has grown in asserting that the persons who objected about length, technicality, or lack of boxed material in some of the articles I have written (or, as here, very extensively rewritten) were proposing a cure worse than the alleged disease. At least in its present state article isn't really so long, and I worked hard to make it well organized.
As for the second idea, if you think you can add a few clear and concise paragraphs at the end of this article about representations of the Lorentz group (maybe just giving a brief overview and the list of possibilities, with a good citation, perhaps to Fulton and Harris), by all means give it a whirl. Or, if you have in mind a long article just on representations of the Lorentz group, well, this is probably the one topic which might really deserve it's own article, so if you want, go ahead and write that and I'll eventually write a concise summary as a section at the end of this article.
But please, whatever you do, do not split off the subalgebra stuff. If you don't appreciate the importance of that discussion, that's only because you haven't read the same books and papers I have, where this is essential!
Another space consideration to bear in mind: when I (or someone else) gets around to writing a proper math article explaining the connection between flows (local R actions) on smooth manifolds, first order linear differential operators, and vector fields, the paragraph beginning "perhaps it might be useful" can be replaced with a suitable link. This will partly make up for the proposed section to be added at the end on representations.
About the proper goals of this article: I write a lot of relativity related stuff and read even more, so I think I stand upon solid ground in saying that a really useful survey of the Lorentz group has been sorely lacking (on the arXiv, for example). Various papers collect bits and pieces, but none offers anything approaching concise coverage of all the aspects of the Lorentz group which come up most frequently in contemporary math/physics. Similar comments apply to chapters in books such as the one by Hall. I worked hard to make this article a balanced but reasonably comprehensive survey, while keeping things concise. My goal is to have every important aspect of the Lorentz group discussed clearly and concisely in one place. (The citations give more detail on various points I mentioned.) I recongize that assessments of relative "importance" may be subjective, but at least my judgement is based on much reading and computational experience.
Actually, in terms of the topics covered, I view this article as something of a model for other articles on other specific Lie groups of great importance. Such topics as subalgebras, invariants, Kleinian geometries, point symmetry groups, bundle structure, as well as representations, are all very important both historically and for contemporary math/physics. Some of these topics tend to be harder for graduate students to appreciate because they are so interdisciplinary, but the value of this material will ultimately become clear to those who continue to work with Lie groups. In my proposed articles on the nine isomorphism classes in the Bianchi classification (of all three dimensional real Lie groups), I intend to discuss similar topics (ten articles, one for the classification, with helpful tables, and nine for each of the classes; as I already said in some talk page, these are sufficiently interesting and important in math/physics to deserve their own articles).
Just to clarify something else: as I read more widely in the math/physics pages, I see there is widespread agreement that the Wikipedia can be both a general purpose encyclopedia and a specialized one, as well as source of up to the hour information on topics of unusual interest. I certainly try to bear in mind the needs of all readers, and I've read the tutorials which suggest for example a "broad to narrow stroke" approach, and I think I've followed these imperatives in this article about as well as anything else I've seen elsewhere on Wikipedia (so far).
Let me ask for feedback on something--- in the introduction, I added a pedantic comment in anticipation of an objection which would not be unfair but which now seems fussy and distracting. Now I think that comment should probably be moved to (the top of) this page. Does anyone want to keep that remark where it is?---CH (talk) 22:33, 10 July 2005 (UTC)

Okay, just a suggestion. I was actually thinking more in terms of readablity then length. The length doesn't really bother me. Certainly, a little more needs to be said about the Lie algebra. Although you object to Linas's notation for the Pauli matrices (see below), I think it is wrong not to include mention of the matrices themselves in this article. The fact that {σk,iσk} generate the Lorentz algebra is both important and useful. For the math student who hasn't seen these before, it takes only 10 seconds to look at the definition and be satisfied.

Regarding the introductory pedantic comment, I have no objections to removing it. I think it adds very little. -- Fropuff 03:20, 11 July 2005 (UTC)

Hi, Fropuff, I have made both changes (adding and subtracting one paragraph for no net gain in length, hurrah!)---CH (talk) 07:43, 12 July 2005 (UTC)

Non-standard treatment?

I am somewhat surprised on skimming the new article that no mention is made of the spinor component notation. These are the Pauli matrices

\sigma^\mu_{\;\;\dot{a}a}

with the vector index μ running from 0..3 and the spinor indeces a and \dot{a} running from 1,2. Thus a four-vector xμ could be represented by a pair of spinors by making the contraction

x_\mu\sigma^\mu_{\;\;\dot{a}a}

and likewise a pair of spinors could be made into a vector. I really liked this notation, as it made very clear that there are two distinct reps, a complex 2-D and a real 4-D rep, and that it was the isomorphism of lorentz to SL(2,C) is actually given by 4=\overline{2}\otimes 2. It also makes clear how SU(2) is a double covering of SO(3). It also provides a bridge to the reps of SU(3) via \overline{3}\otimes 3=8\oplus 1 which is important to quark physicists. Back when I was learning supersymmetry, the vector-spinor-index notation was de-rigeur. So I am somewhat surprised to not see this in this article. All in all, coming from an old-fashioned physics background, this article, as currently structured, comes off as a very non-standard treatment of the Lorentz group that would leave many practicing physicists scratching thier heads.

Let me put it another way: the intro mentions Maxwell eqns, special rel, and Dirac eqn. None of these require any knowledge of the parabolic/elliptic/etc. distinctions. Nor do these need the the Bianchi subgroup bits or talk about stabilizers. The third requires the spinor algebra notation, but little else. So the article promises to talk about physics, but then does anything but. The night-sky null-vector bit is interesting, but would normally be considered a curiosity ... yet it gets prominent billing in the article. This is confusing. linas 01:53, 11 July 2005 (UTC)

Let me put it a third way: physicists are usually insterested only in the spin-1/2, the spin-1, the spin 3/2 (the supersymetric -ino/gauge ghost things) and spin-2 (the GR tensor). The current article fails to distinguish spin 1/2 from spin-1 and makes no mention of the other two. linas 02:27, 11 July 2005 (UTC)

Sigh... Linas, the adjectives "standard" and "important" are somewhat subjective or even "cultural". In this article, I have been trying to bring together concepts from the math and physics worlds which would be better understood by everyone if it were not for certain artificial notational barriers. Trust me, by no means every math student ever takes a physics course at all, and therefore by no means does every math student ever encounter even a mention of Pauli matrices. If you modified my notation to use Pauli matrices, you would exclude all those people. Please don't do that. On the other hand, every math student encounters Möbius transformations, and I think physics students are more likely to have seen these, say in a complex variables course, than math students are to have seen Pauli matrices.
Some of us also want to promote more modern notations, especially where this goal is consistent with making an article as accessible as possible to a wide audience. I think you might be underestimating the thought I put into the organization and notation of this article in its present form.
Please trust me, the night sky stuff is not at all uninteresting to the majority of students. To the contrary, in my experience, most students find this the most fascinating topic of all. It's great that you are fascinated about Fuchsian groups and all that, and this is not unimportant, but I wish you would trust my own experience and judgement a bit more than you seem inclined to do.
You are obviously very eager to jump in and contribute to the article, but we have very different viewpoints. For example, I am trying to stick close to matrix groups, which I think will appeal to the widest possible audience for this article. But many others prefer notations using Clifford algebras or Pauli matrices, especially when discussing representations. Also, for some purposes real representations are more important than complex ones.
You are right that the Pauli matrix notation is very common, and at the present time it is fairly standard in physics, so it should be explained someplace in Wikiepedia. So how about this: would you agree to leave this article alone, and to write your own article on Representations of the Lorentz group, which I will agree to leave alone? You can write that using the notation preferred by physicists (and by many mathematicians who have taken lots of physics courses, or who talk to physicists a lot), Pauli matrices. I'll write a short summary for this article avoiding that notation (which I believe would be harmful to my goal of helping math and physics students talk to one another about the Lorentz group).--CH (talk) 02:43, 11 July 2005 (UTC)

Hey, Sorry, I was not trying to question your experience or judgement. This is not its not a bad article; seems you did a good job. But you deeply misunderstand what I'm interested in and where I'm coming from; I have absolutely no desire whatsoever in writing about the Lorentz group; my interests lie elsewhere; this conversation is a pleasent distraction with a newcomer to wikipedia. I applaud your work; I'm glad you're here; I was merely trying make helpful comments.

However, I am under the impression that most math students couldn't care less about the Lorentz group; they study other things. The people who really care about the Lorentz group are physicists. There are two classes of physicists: those who need a text-book style treatment so that they can design particle accelerators or teach Maxwell and Dirac equations. For them, a clear statement of representation theory matters, and this article is currently lacking clear talk about representations. The other class of physicists are the string theorists, who are interested in Riemann surfaces and Fuchsian groups and the like; but thier level of needs and understanding are a few light-years beyond this article. Its not clear that either group is very well served by the current article. Don't get me wrong, if I was back in school hitting this for the first time, I would find it absolutely fascinating. Its a good article. But if I was in school, I'd also be concerned at how little it overlapped my textbooks. OK, now for the hard knocks: the current treatment is very different from e.g. the Moshe Carmeli treatment or chapters 10,11 of Fulton & Harris. There are standard names for the generators of the algebra, these aren't even named in this article.

I would have been happier if the effort put into conjugacy classes had been put into the article on the Mobius transforms instead, which duplicates a lot of this material. The treatment of the Lie algebra is also unusual; a more standard treatment talks about the structure constants and the generators. The bit about subgroups, covering groups and topology could indeed be moved to another article. To conclude, let me be clear: this is a good article. But as to culture and subjectiveness, WP readers are seeped in culture; I won't be the first or last to think or say what I just said. Although I've already said far far too much.

OK, in fact, I write really bad articles, but that's me :) I hold everyone else up to a higher standard. So yes, I live in the proverbial glass house, and yet I'm chunking rocks. Really, glad to have you here. Please take this kindly. linas 04:53, 11 July 2005 (UTC)

Linas, it's all very well for you to suddenly say
  • you have absolutely no desire to write about the Lorentz group (?!),
  • this discussion has merely been a distraction for you (gosh, what about me?),
but given the many strong opinions which you've expressed on this page about what topics you think should be covered in an article on Lorentz groups, what notation should be used, and so forth, I rather think you have acquired an obligation to write the suggested companion article on Representations of the Lorentz Group according to the vision which you have rather passionately expressed on this page. In fact, I'm calling on you to do just that, and I hope others will speak up here to echo this. I've already said I think you have made some valid criticisms, but clearly I cannot write the article you want so much to see; ultimately, only you can do that. You say you write "really bad articles", but even if that is true, there's only one way to improve your expository skills.---CH (talk) 04:31, 12 July 2005 (UTC)
Ah, well, I'll think about it. linas 14:30, 12 July 2005 (UTC)
Not good enough. If you want to talk to me again, you'll do it---CH (talk) 00:10, 13 July 2005 (UTC)


Help!

I've only been participating in Wikipedia for month or so. It's horrible that I am already involved in some kind of edit war.

A few weeks ago I completely reorganized and added much, much new material to this article. I thought hard about what to say, how to say it and in what order, what notation to use, etc. I worked really hard on this article. My goal was to collect and clearly present the most generally useful facts (for a broad audience) about the Lorentz group in the most elementary way possible. For example, I conciously attempted to remain as far as possible in the world of matrix Lie groups, because most undergraduates are far more likely to grasp matrices and systems of ordinary differential equations than more abstract concepts from graduate level Lie theory courses or string theory courses which I feel belongs in companion special topics articles written to address the needs of more sophisticated audiences.

A user called Linas seems to have a very very different ideas about the goals of an article on the Lorentz group. For example he complained above that in this article I've ignored the needs of students of string theory. Likewise, he has every different ideas about what topics should be emphasized. In particular, he wants to see in this article much, much more about representations, including infinite dimensional representations(!), than I do. As should be clear from the above, I too would in fact like to see at least one companion article on a special topic which is very important but too complicated to discuss in this article without unbalancing it. Accordingly I proposed what I feel is very reasonable procedure which I would hope could make everyone happy:

  • I link to a new article called Representations of the Lorentz Group, in which he can summarize the first six chapters of the book he cited, the book by Serge Lang, or whatever else he wants,
  • he writes that article as he sees fit, and I will leave it entirely alone,
  • he leaves this one alone.

I even said I was going to add a few paragraphs on representations to this article, giving my own very brief summary of the basic facts, which I am confident I can do in a way which fits in gracefully with the rest of this article.

Unfortunately, it seems that Linas wants to delete material which I worked hard to include and to explain in an elementary way, in favor of much more advanced material which he wants to add. However, adding this material in my view would

  • unbalance the present article,
  • break up the flow of the exposition which I worked so hard on.

Is it really too much to ask that Linas adhere to my request above, given that I've worked very hard on this and given that he and I seem to have completely different visions about what to say and how to say it? Is there someway to appeal to the Wiki maintainers to mediate this dispute? Unfortunately, by now I am so disgusted by my interactions with Linas that I want nothing to do with him ever again, but perhaps someone who "knows" us both (on Wiki) can relay my request as above.

Again, I stress that I myself believe that there is a great deal one could legitimately say about the Lorentz group, and I conciously chose not to attempt to say very much in this article about some important topics, particuarly representations. After all, the Lorentz group and its closest relatives, particularly SL(2,C) has been the subject of entire books from various points of view, books which string theorists must perhaps master. So I think that breaking up articles into an elementary one (this article) and the more elaborate one focusing on the needs of string theory students, which Linas outlined above, is a very reasonable solution.

Does anyone other than Linas really think that my proposal is unreasonable?

Is there some formal appeals process for mediating this dispute?

Thanks!---CH (talk) 04:24, 17 July 2005 (UTC)

Well, I think you are being a little prickly about this, actually. An article on the Lorentz group should at least mention the representation theory. One of the basic principles of Wikipedia articles is to aim for completeness; and to indicate, at least, what else there might be to say. That is, we don't really recognise 'closure' of articles. The representation theory is not just used in string theory, surely: it goes back 60 years or more in quantum theory. Charles Matthews 05:27, 17 July 2005 (UTC)
Also I think the NPOV tag is not appropriate here. Is anyone really saying that the current content is not 'written from a neutral point of view'? I don't think so. That tag should not be used just because there is some discussion about the extent of the article content. Charles Matthews 05:32, 17 July 2005 (UTC)

Charles, please, this is really getting frustrating. I don't know how I could possibly have made it clearer that I feel that the basic facts about representations of Lorentz group should be briefly described in an elementary way in this article. I even said that I intend to do this. The dispute with Linas is what I said it is above: whether to remove the material I added (see the history page) and replace it with high level material on representations, which I think inappropriate, or to have Linas write a companion article.

Give me a chance, OK--- I have other pans in the fire, and I didn't get to it 20 minutes after writing the above. Just wait and see what I do in the next few days, OK?

As for NPOV tag, well, one of the pans I just mentioned was searching for information about dispute tags. The proposed "inclusion" template would have been perfect, but apparently that proposal was rejected long ago.

Thanks for your comments, but you failed to say whether you agree with my proposal? If so, what don't you like about it? (Maybe you should reread the entire page above to make sure you have a reasonable idea of what issues I have in mind, which have already been discussed, such as length.) And can you help me with my question about how to resolve this dispute? I am trying to avoid an edit war with Linas.---CH (talk) 05:45, 17 July 2005 (UTC)

Well, I think the content matter can be dealt with, and not so far from your suggestion(s): mention here with a short section, and perhaps have a dedicated page to which that section links (I'm not too clear right now about how much is already out there, for example in relation to the Poincaré group, in some of the theoretical physics articles). I'm aiming to get some basics understood: this is not an 'edit war' by WP standards, just a content discussion based mostly on a possible distribution of content over more than one page. Linas is entirely within his rights to add to this page, and put his view on its development. Your reference to Wiki maintainers seems to show some misconception as to how things are done. There a mediation avenue, but this discussion hardly merits invoking it, at the stage where we are still exploring a couple of conceptions and how the content might fit with other pages. And, let me say, length is not (any longer) a fundamental constraint to articles, so that there is no particular need to see this in terms of one topic pushing out another. I appreciate the work you have done on this page; I am going over these points explicitly, since you might be more comfortable working here with a fuller view of the typical modus operandi. Charles Matthews 08:26, 17 July 2005 (UTC)

Hi, Charles, thanks. I don't really disagree with anything you say, but given the concerns on my talk page I have concluded that I am not after all cut out to contribute to Wikipedia. (I've tried to explain this at some length on my user page.)

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