Talk:Lorentz group/Archive

message: We read: Lorentz transformations which ... preserve orientation are called proper, and as linear transformations they have determinant +1.. It is unclear whether the "proper" transformations are those of the restricted group, whch preserve orientation, or those of the restricted group plus those which reverse orientation and time, which have determinant +1. 87.240.241.192 (talk) 13:45, 18 October 2012 (UTC)
thread_title: Proper Group

message: 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)
thread_title: ToDo

message: 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)
replies: text: 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)
thread_title: Connectedness

message: 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)
thread_title:  Representations and Invariants 

message: 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)
replies: text: 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)
replies: text:  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, \Gamma_d = PSL(2,F) where F = O_d 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)

text: 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)
thread_title:  Quibbles over Terminology: Complex Closed Curve, Bianchi Group, Kleinian Group 

message: 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)
replies: text: 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)
thread_title: Split?

message: 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)
replies: text: 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)

text: 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)

text: 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)
thread_title:  Help!