Talk:Oscillator representation

Just B-class?

This article looks very well written and for a math article, is quite well cited. What is preventing this article from being A-class or a good article nominee? More history? more introductory exposition? --Mark viking (talk) 20:38, 22 April 2013 (UTC)

Thanks. As the main contributor, I am not interested in working up any article to either "good article" or "featured article" status. I am, however, improving other related articles to deal with the theory beyond SU(1,1), especially the semigroup properties and the method of reduction to copies of SU(1,1). That is a slow process and involves the theory of Olshanskii semigroups, symmetric cones, invariant convex cones, Hermitian symmetric spaces, complexification (Lie group) and Jordan algebras, etc. While groups obviously play an important role, the subject of the article is not "in particular group theory," as it is more about analysis, geometry and quantum mechanics than algebra. Mathsci (talk) 02:18, 23 April 2013 (UTC)

It does not meet the B-class criteria: Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Grading scheme For B-class:

"The article has several of the elements described in "start", and most of the material needed for a complete article; all major aspects of the subject are at least mentioned. Nonetheless, it has significant gaps or missing elements or references, needs substantial editing for English language usage and/or clarity, balance of content, or contains other policy problems such as some minor neutral point of view (NPOV) or no original research (NOR) concerns. With neutral point of view, a well-written B-class may correspond to the "Wikipedia 0.5" or "usable" standard.

"Useful to most, but not all, readers. An interested reader flipping through the article may feel that they generally understood the topic. However, it may not be as accessible as it could be, or it may be inadequate for a serious student or researcher trying to use the material, who might have trouble or risk error using the article in derivative work.

"Some editing is still needed, including filling in some gaps or correcting policy errors. Articles for which cleanup is needed will typically have this designation to start with. May be improved by input from experts to assess where coverage is still missing, and also by illustrations, historical background and further references. Consider peer review or nominating for good article status. If the article is not already fully wikified, now is the time.

It fails badly at the "interested reader flipping through the article may feel that they generally understood the topic." It might be closer to C-class

"Useful to many readers. A reader would feel they generally understood the basics of the topic, but there are noticeable gaps in the material presented. There may be questionable or irrelevant material or the material may not be organized in a way that makes the subject easy to understand. Will be of little or no use to a serious student or researcher. "

Without some guiding text " material may not be organized in a way that makes the subject easy to understand" seems an appopriate description. --Salix alba (talk): 19:49, 5 July 2020 (UTC)

Salix alba, on your user talk page I tried to explain some mathematics to you. I wrote to you about the Stone-von Neumann theorem, the Weil representation, the metaplectic representation, etc. When I tried explaining things to you, it was of no interest to you. I have added quite a lot of content to wikipedia, particularly in mathematics. I'm not interested in nominating articles for GA or FA. So the sermon you have written is wasted on me. Your manner seems extremely adversarial. My advice yet again is to learn about the Stone-von Neumann theorem, Weil representation, Metaplectic representation, etc. Mathsci (talk) 20:49, 5 July 2020 (UTC)

I just tried the link to Metaplectic representation. It was a redirect to Oscillator representation. That redirect was created by User:R.e.b. He told me privately why he had stopped contributing to mathematics articles on wikipedia. But, presuming you know who the user is, why do you think the redirect was created? In the article there is a fairly well-known book Vergne and Lion on the Weil representation. Salix alba, what position are you in to pass judgement and why are you doing it? Mathsci (talk) 20:49, 5 July 2020 (UTC)

I'm more interested in each of the individual sections. One paragraph for each section explaining how this

section contributes to the whole story. Why is there a section on Fourier transform? Why is their a section of Holomorphic Fock spaces? May be it makes sense to someone familiar with the material, but for someone news to this, our target audience, its as clear as mud.

As to you assertions to my motivation it is not relevant here. I'll discuss it on my talk page.--Salix alba (talk): 21:37, 5 July 2020 (UTC)

All of these topics are discussed in Folland's Harmonic Analysis on Phase Space, which summarises the article. The Stone-von Neumann theorem implies that there a number of different ways of realising the unique irreducible representation of the Heisenberg group. One of those ways is through the holomorphic Fock space: that is where things fit in. Your use of words like "as clear as mud" is not helpful. Holomorphic Fock space is explained on Folland's book with citations. Other editors have used the section on Oscillator representation as a redirect to Holomorphic Fock space. That means that somebody has found it useful. The Fourier transform arises because of its role in the Stone-von Neumann theorem. The group $SL(2,R)$ realised on $L^{2}(R)$ can be identified with a group of Möbius transformations. The element for the transformation $-1/z$ in the oscillator representation is the Fourier transform. Mathsci (talk) 23:28, 5 July 2020 (UTC)

I am slightly confused by who chose the category on this take page as "geometry", which is obviously wrong. The categories for the article are "operator theory", "harmonic analysis", "representation theory", "quantum mechanics" and "theta functions", as is the case now. Mathsci (talk) 23:58, 5 July 2020 (UTC)