Talk:Stone–von Neumann theorem

What's happened to this article?

 * so that saying it is 'small' isn't very meaningful...

I'm not sure I understand what this means, particularly since asymptotics (e.g. $$ h \rightarrow 0 $$) are an important topic in quantization theory.CSTAR 16:13, 23 Jun 2004 (UTC)

It has the dimensions of action, rather than being dimensionless; that's all I really meant.

Charles Matthews 16:37, 23 Jun 2004 (UTC)


 * Fair enough. Maybe you should say that in the article.CSTAR 16:51, 23 Jun 2004 (UTC)

I hope I got the constants right on the Fourier transform. CSTAR 22:31, 27 Jun 2004 (UTC)

I wonder if it needs much more to construct the Weil representation, which is a requested article. Charles Matthews 15:08, 29 Jun 2004 (UTC)
 * I was planning on doing that under the metaplectic representation in the not too distant future. I also added the Poincaré-Birkhoff-Witt theorem which is a particularly important fact.  I'm wondering what the distinction between a featured article and a non-featured article is? Should I care?CSTAR 15:28, 29 Jun 2004 (UTC)

It's like a five-star hotel, I suppose - one knows it will cost more, and it may even be better. Charles Matthews 15:55, 29 Jun 2004 (UTC)
 * Hmmm. I think one can reliably say that about five-star hotels (at least in France) that they may be better, but I've seen some featured articles with numerous innaccuracies.CSTAR 16:16, 29 Jun 2004 (UTC)

Nit: position and momentum are reversed
Uhh, this is kind of a nit, but in standard physics usage, Q is the position coordinate, and P is the momentum. (p^2/2m is the kinetic energy/schroedinger operator/laplacian, p-slash is the dirac operator, p is the momentum part of the energy-momentum tensor). I'd fix this myself but verifying all the minus signs in this article is daunting .. linas 04:56, 2 Mar 2005 (UTC)
 * Hmm. I think you're right.. I don't know what I was thinking. But it may not be that hard to fix.  Although the results are true as stated and equivalent to the the other form with P, Q interchanged. CSTAR 05:05, 2 Mar 2005 (UTC)


 * OK, great, thanks, it was late at night, I was going to fix it this morning...linas 15:35, 2 Mar 2005 (UTC)

plancks const and Im tau
I was adding to the article on theta functions (and am not done yet) (and should probably move some of that content to the article on heisenberg group) and there's a G-module isomorphism, in the texts I'm reading (mumford), there is no plancks const (its not mentioned, and crudely seems to be taken as one). But in one relationship, it seems to also be related to Im &tau; (maybe even equal to Im &tau; ??) where &tau; is the thing appearing in the article on theta function. Ever see anything along these lines? Any words of wisdom?linas 15:35, 2 Mar 2005 (UTC)

See also the section on S, T in theta function; I'm thinking that roughly Q=T-S Re &tau; and P=S+T Re &tau; or something like that ... is there a canonical form for this relation? I don't want to mess it up by just making one up that seems to fit but is subtly wrong... linas 15:35, 2 Mar 2005 (UTC)

Operator hats
The first section (after the lead) would benifit from decoration of the operators with operator hats. For example, the leftmost x in the first equation has a meaning distinct from the rest of the x's in that equation. Only in the "x-basis" do the operators look like here. In the momentum basis picture, the expressions look about the same but with p<->x and a sign change somewhere.

The notation in the article is of course used in any and every QM book, but this is usually only after the standardized abuse of notation has been explained. YohanN7 (talk) 08:31, 14 September 2012 (UTC)
 * Agreed, and see comments two topics below below about "P","Q" vs "p","x". 178.38.159.243 (talk) 00:53, 10 May 2015 (UTC)

Typo?
The right hand side of the second relation of Ref 1 has two vertical bars || on the right but one | on the left. Is this O.K. or am I missing something? Xxanthippe (talk) 00:03, 11 March 2013 (UTC).
 * Under any magnification? they are all plain operator normsCuzkatzimhut (talk) 02:32, 11 March 2013 (UTC)
 * Thanks for your prompt response. I missed the zoom. It might be helpful to readers with poor eyesight or poor computer monitors if you could make the two vertical bars on the left larger. Xxanthippe (talk) 04:25, 11 March 2013 (UTC).
 * Sorry, I'm sorry I can't, too efficiently... Would you like to experiment? The point is the math mode used is meant to adjust to one's computer's local conditions, and it looks fine on mine, so i can't be the judge of its adequacy on yours...maybe inserting big /big tags? maybe you could select bigger fonts for all your browsing settings in wikipedia prefs? It would not be a tragedy if you turned it to plain HTML, instead.   Cuzkatzimhut (talk) 10:57, 11 March 2013 (UTC)

Usage of P, Q vs p,x
In the section "Uniqueness of representation", P and Q are used at the start for general operators satisfying the equivalence relation, but then later they were used to refer to the concrete p, x of the previous section. I corrected this by changing the latter P,Q to be p,x.

But the usage is still not consistent towards the end of this section. It needs further small corrections.

178.38.159.243 (talk) 00:51, 10 May 2015 (UTC)

Anticommutators?
Fermion fields satisfy anticommutation relations (CAR) instead of commutation relations (CCR). I might add a link to CCR_and_CAR_algebras because this is a relevant generalisation to know about. — Preceding unsigned comment added by 130.199.100.158 (talk) 20:03, 29 August 2018 (UTC)