Talk:Lorentz group

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[edit] Old Discussion Archived

This article was changed beyond recognition when I greatly expanded it in July 2005 (and I still have more to do). Unfortunately, in the middle of this process, a serious misunderstanding arose which led to a bit of a kerfluffle. Fortunately, this has been mediated, and I don't think the "flap" is very edifying, so I have archived it at Talk:Lorentz group/Archive.

Please add any comments/suggestins on present article below. I've put in a lot of work on this, so I hope all good Wikipedias will ask me for a response before making major changes. TIA---CH (talk) 04:47, 6 August 2005 (UTC)

[edit] Left/Right groups?

What is meant exactly by the left and right groups in the double covering SU(2) → SO(3)? -- Fropuff 06:02, 14 October 2005 (UTC)

You still haven't answered my question CH. This needs to be clarified. At any rate the section on topology needs to be corrected: SO+(1,3) is a trivial bundle over H3; there is no "twist" (any fiber bundle over a contractible base is trivial). -- Fropuff 18:44, 23 January 2006 (UTC)
Sorry, I guess I didn't see your comment before. Yeah, this could be clearer! I meant left and right side of the arrow, not left and right multiplication. Feel free to untwist! A reference specifically discussing the topology of the restricted Lorentz group would be useful. I don't have Hall's book in front of me but there might be something useful in there.---CH 16:20, 24 January 2006 (UTC)
Ahh! Thank you. I couldn't figure out what in the world you meant by that. -- Fropuff 16:30, 24 January 2006 (UTC)

[edit] Topology

The article does not state which topology is used for the Lorentz group but mentions connection properties which depend on the topology. I assume it is topology induced by the operator norm which is the same topology that results when the Group is viewed as a finite dimensional vector space? The Infidel 10:41, 21 January 2006 (UTC)

The topology of O(3,1) is the subspace topology inherited from GL(4,R), which itself can be viewed as an open subset in R16 (with the Euclidean topology). The Lorentz group is not a vector space (but it sits inside one), so I'm not sure what you mean by that last statement. -- Fropuff 16:38, 21 January 2006 (UTC)
Thank you. The last statement should be "as (topological) subspace of a finite dimensional vector space". I think we should mention the topology briefly in the article. Any objections? The Infidel 20:17, 22 January 2006 (UTC)
Hi, Infidel, I don't understand what you found confusing about the existing description. Why did you think I might be refering to functional analysis in the context of a finite dimensional real Lie group? Have you seen the book by Hatcher which I mention in the references?
If I understand what you found confusing, I can try to improve this bit myself. I'd like to try to keep the style and emphasis as internally consistent as possible, which probably means that wherever possible I should make any neccessary changes myself.---CH 01:07, 23 January 2006 (UTC)
I have no special background of Lie groups, so I just wondered on which topology the unconnectedness is based. And shortly my mind went astray considering open-compact topology and the like ... The Infidel 18:32, 23 January 2006 (UTC)

[edit] Students beware

I completely rewrote the August 2005 version of this article and had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article 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. I hope for the best, but unfortunately relativity theory attracts many cranks, and at least some future versions of this article are likely to have been vandalized or to contain slanted information, misinformation, or disinformation.

Good luck to all students in your search for information, regardless!---CH 01:50, 1 July 2006 (UTC)

[edit] Lie algebra

"its Lie algebra is reducible and can be decomposed to two copies of the Lie algebra of SL(2,R)"

Really? sl(2,R) has rank 1 (because it contains so(2)), so sl(2,R)^2 has rank 2, but so(3,1) has rank 1 (since sl(2,C) has rank 1). What's going on here? Adam1729 07:18, 2 October 2007 (UTC)

[edit] Conjugacy classes

There are infinitely many conjugacy classes. Every rotation of order m is in a different conjugacy class from every rotation of order n. I suspect that when the article says "conjugacy class" it really means "topological closure of conjugacy class". Is this right? Adam1729 07:24, 2 October 2007 (UTC)