Talk:Canonical quantization

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Contents 1 First vs. Second 2 Equations 3 Style mods 4 Empty sections 5 Merge some material with another article? 6 All other commutators vanish? 7 Some comments

[edit] First vs. Second

I really suggest splitting this article into two; one on the canonical quantization of finite-dimensional systems, and one on inifinite-dimensional systmes (second quantization). Seems that most of your plans are for second quantization, e.g. the empty sections on amplitudes, perturbation theory.

Note also, re quantum mechanics, the quantization is an art, not a science. You have to guess correctly what a good set of canonical coords might be, you have to guess how to replace the poisson bracket by the commutator (see e.g. Moyal product); its not clear how to extend to higher order terms in h-bar. There are no prescriptions on how to make this stuff work, that's why I called it "ad hoc quantization" on the other talk page. Don't make it out to be cut-n-dried, its not. This is why we have an article on quantization to begin with. linas 15:13, 6 Jun 2005 (UTC)

[edit] Equations

I think that is necessary, first above all, to write the equations in the proper latex typography. Then, I agree with the position of splitting the article. josemiotto 18:10, 3 Jul 2007 (Buenos Aires Time)

[edit] Style mods

I accept both your points and have suggestions for incorporating them:

• The article on quantization is an overview and therefore describes what is known and what is open: as you had planned earlier. This leaves individual articles (like this) to make the more cut and dried presentation...
• However, to alert the reader that there are open questions, in the history section, add pointers to developments which showed these difficulties.
• Also add a section where one well-chosen example of each kind of problem is discussed, and lead from there back to the quantization article. From my perspective, I could discuss the Gribov problem here. You could add an example where there is an ambiguity in the choice of canonical coordinates.

I see that some of the points you are making here would also go into the articles canonical commutation relations, canonical conjugate variables and CCR/CAR algebra, where you have been making contributions. Perhaps it is also possible to pull those articles together into a single comprehensive one, where these points could be made. That would serve as the split that you suggest. (The reason it would be nice to keep the small section on QM here is that it adds to the discussion on QFT. It would be possible then to limit the size of this section here, and refer to the companion article for details.)

If this is acceptable, then this could set the pattern of the remaining pages as well. In particular, I can see that this pattern of exposition would apply to the lattice field theory and path integral articles. Bambaiah 05:38, Jun 7, 2005 (UTC)

Sure I guess. The only other comment is that the section called "Mathematical quantization" is about first quantization; having it appear after a long section on second quantization just sort-of buries it. Maybe the simple quantum mechanics intro you this article could be moved or copied to the intro for Quantization (physics) to provide a college level intro; and the section "mathematical quantization",also moved back, as a more formal way of saying a similar thing.

For your enjoyment, two articles I've worked on/puzzled were Heisenberg group (which follows from the CCR) and a curious representation of the Heisenberg group by the theta functions. Theta functions lead directly into number theory, and the Heisenberg group is the prototypical example of sub-Riemannian geometry, where occasional interesting things happen (e.g. the Berry phase, if you remember that craze). linas 14:34, 8 Jun 2005 (UTC)

[edit] Empty sections

The sections 'Computing amplitudes' and 'Renormalisation' seem to be empty. Are they going to be filled, or should they be deleted?

They've been sitting vacant quite a while. Delete them, they're easy enough to put back in. linas 23:19, 28 July 2005 (UTC)

[edit] Merge some material with another article?

There's a related article Creation and annihilation operators which might have some material better suited for this article... --HappyCamper 05:47, 31 July 2005 (UTC)

[edit] All other commutators vanish?

This says to me that [a_k, A] = 0 for arbitrary A != a_k^*. Should this perhaps say that [a_k^*, a_k'] = \delta_{k k'} and [a_k', a_k] = [a_k'^*, a_k^*] = 0 ? Or could A be any operator?

[edit] Some comments

replaced by commutators, ih/(2π)[q,p] = qp-pq = 1.

maybe here one should make it more explicit that this is a property of the two operatoers used and not of the commutators in general.

The states of a quantum system can be labelled by the eigenvalues of any operator.

This is mathematically incorrect, you cannot do this for any operator. The property of having eigenvalues and being able to express states by (infinte!) sums of eigenvectors is special to the operators used here. Although this may not be relevant to physics and the content of the article one should avoid false statements. —The preceding unsigned comment was added by 217.216.48.51 (talk) 12:23, 2 March 2007 (UTC).