Talk:Algebraic quantum field theory

Is the functor $$\mathcal{A}$$ covariant, or contravariant (as it would be in the case of a sheaf)? It perhaps looks like the former, from what is said (restriction maps are rarely going to be injective). But I think we should be told.

Charles Matthews 12:56, 1 Dec 2003 (UTC)

Aren't functors automatically assumed to be covariant by default unless explicitly told otherwise? Phys 13:33, 2 Dec 2003 (UTC)

Yes - but the notation i-sub-stuff wasn't introduced explicitly, making it harder to suss out.

Charles Matthews 17:17, 2 Dec 2003 (UTC)

does AQFT stand for axiomatic quantum field theory?Lethe

Apparently algebraic QFT, though it is also axiomatic.

Charles Matthews 18:34, 12 Jun 2004 (UTC)

I'm somewhat unsatisfied with this article but don't know how to proceed. So I'll start on the discussion pages (in fact I added a link before I got my user account and did a small change on QFT, BTW thanks for sp and fmt).

The entry doesn't read as physics but as pure mathematics. Of course an axiomatic approach has a strong mathematical side, but there's something beyond.

The entry has only the objective side of AQFT, what is IMHO missing are motives, successes, failures relative standing compared to other approaches. Any feedback whether this would be OK to add? Then I'll try to do it.

Pjacobi 21:56, 7 Jul 2004 (UTC)
 * I agree completely. Let's hope there'll be more progress towards this in the next 18 months ! _R_ 19:17, 3 March 2006 (UTC)


 * That is completely the wrong tag (technical tag) for asking for improvements on content (which would probably make the article more technical anyway). I removed it.  --C S (talk) 07:32, 27 April 2009 (UTC)

Also, how does one "pull an action back" to the target category, when the action is defined on the domain category? This does not make any sense, though an equivalent notion could be developed if the functor $$\mathcal{A}$$ were an equivalence of categories. Regrettably, it is not. The Poincare covariance axiom is not well explained in this article and should be reformulated. Haag's famous paper from the 60s would do nicely as a source. myrkkyhammas 18:40, 2 March 2007

List of researchers
The list of researches at the end along with links to their websites seems promotional to me. So I plan to cut down the list to those researchers who are notable as evidenced by an article on them at WP. --Mark viking (talk) 20:58, 20 February 2014 (UTC)

The description is only for category theorists.
The page is written in the language of category theory. I suggest that many people who would be interested in the Haag-Kastler axioms don't speak that language.

FWIW, Haag and Kastler did not present their axioms in the language of category theory.

Gregweeks (talk) 01:43, 25 May 2012 (UTC)gregweeks

Net and net monomorphism need to be defined
Somebody more expert in AQFT than I should explain what "the net" and "net monomorphism" refer to. My general sense is that an AQFT defines an allowed set of states on a "net of algebras" but it should pointed out just what that net is before the term is used. There is a monomorphism referred to earlier, maybe that's the net monomorphism, but then this should be stated. Hope someone can do this!

MorphismOfDoom (talk) 18:51, 7 October 2014 (UTC)

Requested move 20 December 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion. 

Local quantum field theory → Algebraic quantum field theory – New name is much more widely used in the scientific literature and thus more appropriate&#32;STEMster42 (talk) 10:46, 20 December 2022 (UTC) This is a contested technical request (permalink). Steel1943 (talk) 14:23, 20 December 2022 (UTC) The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * This comment thread began at WP:RMTR. Steel1943  (talk) 14:23, 20 December 2022 (UTC)
 * Some quick searches says otherwise, so I do not think this is uncontroversial. UtherSRG (talk) 12:10, 20 December 2022 (UTC)
 * May I ask what did you search? Searching both on Google:
 * https://www.google.com/search?q=algebraic+quantum+field+theory
 * https://www.google.com/search?q=local+quantum+field+theory
 * Shows far more relevant results for the first query than the second. Furthermore if you want an example from another Wikipedia run by academics working in the field (https://ncatlab.org/nlab/show/Haag-Kastler+axioms) it states pretty clearly on the page "The formulation of quantum field theory via these axioms has come to be known as algebraic quantum field theory or AQFT, for short." It also notes the issues with terminology but again looking at the respective pages there (https://ncatlab.org/nlab/show/AQFT) and (https://ncatlab.org/nlab/show/local+quantum+field+theory) you can see algebraic quantum field theory is more appropriate since the latter also can include functorial QFT which is not the main topic of the page. I will also add that recent textbooks in the area all call it algebraic quantum field theory (https://link.springer.com/book/10.1007/978-3-319-21353-8 https://link.springer.com/book/10.1007/978-3-319-25901-7 https://link.springer.com/book/10.1007/978-3-319-21894-6) while the term local as mentioned in the first ncatlab article I linked comes from a book published in the 90s. STEMster42 (talk) 12:38, 20 December 2022 (UTC)
 * I think is right, particularly as it is the accepted term for modern textbooks. Polyamorph (talk) 13:16, 20 December 2022 (UTC)
 * To add a further authoritative reference, recent Snowmass papers (https://arxiv.org/abs/2203.08053, https://arxiv.org/abs/2210.03128) also refer to it solely as Algebraic QFT. Snowmass is a once a decade gathering of particle physicists in the United States where they talk about the future of their field. For more info see: https://www.scientificamerican.com/article/physicists-struggle-to-unite-around-future-plans/ STEMster42 (talk) 14:16, 20 December 2022 (UTC)
 * I did google and gscholar searches of the strings in quotes: Google "Algebraic quantum field theory" Google "Local quantum field theory" Gscholar "Algebraic quantum field theory" Gscholar "Local quantum field theory" UtherSRG (talk) 14:49, 20 December 2022 (UTC)
 * With the Google Scholar links you see most of the references for Local AQFT are much older than than Algebraic QFT ones which reflects how the terminology has changed. STEMster42 (talk) 15:19, 20 December 2022 (UTC)
 * Ping current participants. Steel1943  (talk) 14:24, 20 December 2022 (UTC)