Talk:Local quantum field theory

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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)

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

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