# Talk:Representation theory of the Lorentz group

Dashes instead of a math symbol—namely, «D – 2»—linger for two years, and in multiple instances. Worse: originated not from a clueless editor, even not from a stupid script making blind replacements for U+002D. How can such guru as YohanN7 commit this? Not good… guys, you should learn to manage without me, at the end. Incnis Mrsi (talk) 15:24, 3 May 2019 (UTC)

The section removed here, with Prerequisites outlined and instructive passages like These can be thought of, in the passive view, as (instantly!) giving the coordinate system (and with it the observer) a velocity in a chosen direction, is a clear-cut example of pedagogical material that is inappropriate here per the NOTTEXTBOOK policy: Wikipedia is an encyclopedic reference, not a textbook. The purpose of Wikipedia is to present facts, not to teach subject matter. It is not appropriate to create or edit articles that read as textbooks, with leading questions and systematic problem solutions as examples. Also relevant in the same policy:  Describing to the reader how people or things use or do something is encyclopedic; instructing the reader in the imperative mood about how to use or do something is not
Wikilinks give connections to articles further explaining related topics. It’s not the place of the article to outline prerequisites for learning material; articles neutrally describe facts.  — MarkH21talk 18:42, 5 May 2020 (UTC)

I see your points in principle, but 95% of the bitter  complaints about WP one gets in PSE and places where students congregate are about the imperious, elliptical, click-tag game WP is subjecting them to.  This particular GA article, whose development I watched  with admiration,  has already done yeomanly service for years, reminding physics students of basic facts and jargon, with all the material accessible bypassing the need for out-clicking.
It used to be a go-to reference. Coming in as a mathematician, (and not a physicist, the principal target audience of this article), and declaring  that something is too trivial and pedagogical, even if hidden !, ensures the disappointed students shake their fists and vent more.  I could not disagree with them, as I saw a fine article made less helpful to them in real time, on the basis of highly arguable principle.  Readers and students will move on and away.  Cuzkatzimhut (talk) 00:42, 6 May 2020 (UTC)
It doesn't matter if there are complaints at StackExchange, and my background doesn't matter. The fact of the matter is that, by Wikipedia policy, the Wikipedia is not a textbook and the purpose of Wikipedia is not to serve as a substitute for textbooks and other learning resources. If you disagree with the policy, then take it up at Wikipedia talk:What Wikipedia is not or Wikipedia:Village pump (policy).By the way, article content should never be hidden by MOS:DONTHIDE. I have also never declared any content here as too trivial. Also note that introducing and presenting broader context (in moderation) for accessibility to a topic is fine, but the pedagogical language and presentation style of the removed section is not. — MarkH21talk 02:11, 6 May 2020 (UTC)
The baby should not be summarily thrown away with the bathwater. If you felt you could actually improve the presentation style, you are of course more than welcome to do this,  beyond trashing clarifications that make the article more accessible to a general audience, including physicists, the major consumers of this article, also a policy of WP. Proposing an improved section here would allow the other editors to assess its merits. Cuzkatzimhut (talk) 14:01, 6 May 2020 (UTC)
I think the other sections are fine and sufficient though. Context can be given in the other sections where needed, without a general introduction/prerequisite section. — MarkH21talk 15:04, 6 May 2020 (UTC)
I suppose students could be steered to the Wikiversity link  on the left column of the page. Cuzkatzimhut (talk) 16:56, 6 May 2020 (UTC)
Yes, Wikiversity and Wikibooks are very suitable place to direct students and StackExchange questions. — MarkH21talk 17:12, 6 May 2020 (UTC)

Thank you to all contributes 41.190.245.201 (talk) 13:25, 30 December 2021 (UTC)

I don't want to dive in and make these edits myself because (a) I'm not sure I'm right, (b) a lot of people have clearly put a great deal of hard work into this page and could have better ideas about how my observations could be used, but firstly there seems to be a reference (in the "Explicit formulas: Weyl spinors and bispinors" section) to equation G1, which doesn't exist. I'm pretty sure it should be a reference to equation A2 instead. Also, I think equation A2 is derived from the formulas A=(J+iK)/2 and B=(J-iK)/2 at the start of the section "The Lie algebra", and maybe it would improve clarity if this were made explicit. Lastly, I wonder if it's worthwhile showing an equivalent calculation to W1 for the (1/2,1/2) case, to show how the vector representation comes out of A2. 1.125.111.33 (talk) 01:58, 23 April 2023 (UTC)

It has been a while since this article has been reviewed, so I took a look and noticed the following:

There are uncited statements in the article. Although some of these are covered under WP:CALC, others do needs statements such as the publication of the classification of SL (2,C) and " (tensors and spinors have infinite counterparts in the expansors of Dirac and the expinors of Harish-Chandra) consistent with relativity and quantum mechanics, but they have found no proven physical application.". I can add citation needed tags upon request.
The lead does not summarise all major aspects of the article and is thus too short. Every major section (level 2 heading) should probably have some information in the lead.
At over 9100 words, this article is at the cusp of being too large per WP:SIZE. I recommend that a subject-matter expert review the article and trim or WP:SPINOUT information that could be summarised more effectively or is too much detail for the scope of this article.
Should this article go to WP:GAR? Z1720 (talk) 03:46, 5 November 2025 (UTC)

For size matter, see Talk:Representation theory of the Lorentz group/GA1. Dedhert.Jr (talk) 11:16, 5 November 2025 (UTC)
@Z1720. Can you tell us specifically which unsourced part you mentioned? Dedhert.Jr (talk) 12:02, 5 November 2025 (UTC)
Oh, regarding the subject-matter expert, I suggest you should ask WT:WPM. Dedhert.Jr (talk) 12:20, 5 November 2025 (UTC)
Replying to the first bullet. I think you can consider the "development" section as a lead of the article. That's what I thought whenever I clicked the wikilinks, some of which are supposed to redirect to the sections below. But I am not sure if merging into the lead is a good idea, unless we can ask the around-2017-inactive-nominator. Dedhert.Jr (talk) 13:12, 6 November 2025 (UTC)
@Dedhert.Jr: I have added citation needed tags. In regards to length: I think editors should spin out sections of the article. Several level 2 headings are quite long with lots of sub-headings: these are great places to start looking at what can be moved to other articles and summarised here. Z1720 (talk) 01:04, 12 November 2025 (UTC)
@Z1720. It's a better way to ask WT:WPM regarding the SPINOUT. Neither you nor I could understand the topic. Whether we reduce the number of bytes by cutting off big chunk paragraphs, be understandable even more or otherwise is questionable. We had acrimonious conversations a year, two years ago, or more or less. I don't want to talk about it in more detail before someone else pukes harsh-raged words. Just search it up. Dedhert.Jr (talk) 07:26, 12 November 2025 (UTC)
@Dedhert.Jr: I skimmed through the conversation in the GAN. I am happy to give suggestions with that process if asked. I think the concern is less about understanding the technical aspects and more about summarising information here and then having an expanded explanation in another article: the lead of an article is a summary of what is in the article body and is a good guide on how to summarise information that has been spun out. The article is also just over 9,000 words, so it might not even need to be spun out, but instead just have information summarised more effectively. To be clear, I am much more concerned about the uncited text and won't nominate an article at GAR if the only concern is that the article is at 9,100 words. Z1720 (talk) 14:57, 12 November 2025 (UTC)
For the uncited text, this is treatable: either by removing it or searching the sources before adding the cites. Dedhert.Jr (talk) 05:28, 13 November 2025 (UTC)
On a first reading, I'm not really seeing natural candidates for sections to be spun out. I can look for things to condense, but it's already pretty terse.
At least two of the {{citation needed}} tags could probably be filled by a standard quantum field theory book. Another is the definition of complete reducibility for a Lie group, which is likewise standard and would be given in any textbook about Lie groups. The fourth is about how the Lorentz group itself can be thought of as acting conformally on the complex plane or on the Riemann sphere, which might not be said in quite as many places but which shouldn't be too hard to find in a book, either. Stepwise Continuous Dysfunction (talk) 19:32, 13 November 2025 (UTC)
This article has some major shortcomings that suggest (IMO) that it should not have been classified as a GA.
The lead is more history lesson than about the topic.
The article makes extensive use of topic-specific concepts and notation that it doesn't bother to define.  It does not write one level down.
The article does not even seem to address its own topic; instead, it goes into applications, etc.  What gives?
It is rare for me to feel so utterly at sea when reading a physics-related article, unable to interpret much of what it says and not seeing sufficient leads for building the underlying concepts and familiarity with notation.  It is the kind of article that I immediately abandon reading because I can get no purchase on it for understanding.  It gives the information of being an infodrop by someone who is making notes to self, not following the purpose of an encyclopaedia.  I would drop it to B classification.  —Quondum 20:17, 13 November 2025 (UTC)
I do not understand these complaints. The lede includes history because the article covers the history. The applications matter because this is not just pure math, but math used in particle physics. The notation is standard for the subject. It could be better explained at points, but it's not out of line with any other treatment of the topic that I've seen. I don't particularly care whether or not the article has a green sticker on it; I'm just trying to get a handle on your concerns. What is an article whose prerequisites include special relativity and the Lorentz group supposed to look like, if not this? Stepwise Continuous Dysfunction (talk) 21:24, 13 November 2025 (UTC)
Applications should not be presented before covering the article topic.  I'm not saying that they should not be there, but there literally is nothing before that section and the lead.
I have a pretty strong understanding of special relativity and Lorentz transforms, as well as indexed tensor notation and an adequate understanding of the notation used for groups in this article, as well as the direct sum of groups, so I pretty much satisfy your given prerequisites.  Lie algebras not so much, though I understand these as describing local group structure.
"the (m, n) representations to be introduced below" is the wrong order to present things, and anyway what follows is difficult to wade through to get a sense of what the notation means, let alone assigns a meaning to m and n.
I presume what you mean by "any other treatment of the topic" is a textbook treatment, exactly what WP is not supposed to model itself on.
Maybe I should just withdraw: I am not in the mood to help make this article accessible to one level down, even from the sidelines.  In the past I have repeatedly wanted to comment but refrained because it simply seemed too daunting to engage on this.  —Quondum 22:14, 13 November 2025 (UTC)
OK, I think I am better understanding your perspective now. Thanks.
I could hazard a guess as to why the "Applications" section came first. It kind of reads like providing a motivation for the subject, which is a natural enough thing to do, but perhaps it's the wrong style choice here. I thought about moving it, but some of the ideas introduced in it are used in what follows, so I retitled it and trimmed some formulae.
Physicists do as much as possible with the Lie algebra (the local structure of a group in the immediate neighborhood of the identity) rather than the full, global structure of the group. That perspective was probably a strong influence on this article.
As I understand WP:NOTTEXTBOOK, that means not using rhetorical tricks like leading questions to guide a reader through a subject. My observation here is that the notation is in line with the textbooks I've seen, neither dramatically simpler nor more complicated. I think that's mostly fine. Stepwise Continuous Dysfunction (talk) 23:06, 13 November 2025 (UTC)
I don't have an objection to use of standard notation for the topic, though it should be adequately introduced.  I also do not object to the Lie algebra being used to develop the theory being described; this is merely a description of a personal limitation.  I was thinking more along the lines of WP:ONEDOWN than WP:NOTTEXTBOOK.  —Quondum 23:46, 13 November 2025 (UTC)
@Quondum, @Stepwise Continuous Dysfunction. I'll reply to the lead and the first section of applications. Apparently, I was the one who merged the last three paragraphs, which were once the section of "Development" before "Applications". My interpretation is that these uncited are covering the next sections. I'll see if I can revert the edit. Dedhert.Jr (talk) 23:37, 13 November 2025 (UTC)
Okay, you folks are clearly at work on the structure, so me commenting on it for now will just hamper this.  —Quondum 23:46, 13 November 2025 (UTC)
@Z1720. Okay. I declare keep the status of this article. If you have more comments, let me know. Dedhert.Jr (talk) 04:20, 20 November 2025 (UTC)
@Dedhert.Jr: I have added some additional "citation needed" templates to the article. Z1720 (talk) 14:55, 20 November 2025 (UTC)
@Dedhert.Jr: – Not so fast.  First invite comments of those who care to make them.  I had strong reservations about the original GA status being granted, and I was waiting for your edits to settle before looking again.  And if you want to declare that keep is appropriate, it is up to you to have checked it against the criteria.  —Quondum 15:11, 20 November 2025 (UTC)
@Quondum. Bruh. I have to postpone my vote for now, following the additional tags. Dedhert.Jr (talk) 01:20, 21 November 2025 (UTC)
@Dedhert.Jr and Quondum: Just a note that this is an informal discussion, so editors are just giving suggestions on how the article could be improved and meet the GA criteria. Declarations aren't necessary, but helpful if it makes your assessment of the article clearer. Z1720 (talk) 01:34, 21 November 2025 (UTC)
@Z1720. Oh yeah. I totally forgot we haven't taken this to GACR. Silly me. Dedhert.Jr (talk) 01:35, 21 November 2025 (UTC)
Z1720, understood.  I would likely not get involved in a formal GA review because there is seems to be just too much wrong to comment on.  My contribution in terms of suggestions for improvement even informally is likely to be limited, though I can provide some general observations.  Starting from that this is one of the very few math and physics that have difficulty getting cognitive purchase on.  The title is a bit confusing: is the article about the context of the development of the theory, or does it cover the theory content?  If the former, it is essentially an article about history, and the title should change accordingly.  If it is about discussing the representation(s) of the Lorentz group, the title should change accordingly.  If it is both, then it should be entitled as for the latter, just with a history section.  Its structure is rather like a set of disconnected insights noted by a student during a series of lectures on the topic, each addressing some separate aspect.  They assume a known broader context (such as conventions, notation, prior knowledge, which is missing, but would have been provided in the lectures).  Certain key points are missing, for example in the section § Relativistic quantum mechanics, where the value n remains without context.  Is it the number of dimensions?  The following formula seems to suggest it is, but that uses ill-defined notation that I have never seen elsewhere (in other mathematics or physics articles).  But then why not just set it to 4, which it is in the case of the Lorentz group?  This, and many other oddities, are left unaddressed within the article, making it useless to any reader who is not already an expert previously familiar with all the notation and concepts.  I will not extend the list now, but my concern is that it is long and that this article needs an extensive rewrite to meet WP criteria.  —Quondum 16:16, 21 November 2025 (UTC)