non-pointlike localized observables in Axiomatic QFT

Question

I'm reading Detlev Buchholz, "Current Trends in Axiomatic Quantum Field Theory", LNP 558, pp. 43-64 (Springer-Verlag, Berlin, 2000). He writes that the AQFT "framework proved to be flexible enough to incorporate non-pointlike localized observables, such as the Wilson loops" (page 45).

On page 47, Buchholz extends the non-pointlike localized observables to "such as Wilson loops or Mandelstam strings".

My question: are there other non-pointlike localized observables in the AQFT literature?

Comments

There is a lot about string-localized (and wedge-localized) quantum fields in AQFT. You can easily find references through scholar.google.com. I am fairly sure that it is this what he refers to,

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Sometimes those working in aqft always claim they can do this and do that . But sofar I didn't see how they are able to describe the most important part of physics - the standard model and 4-dimensional qft with interaction.

Answer 1

I do not know what Detlev means in this case. However an easy, perhaps naive,  answer can be done thinking of self-adjoint generators in a GNS representation of a state on a local $*$-algebra of observables when the state is invariant under a continuous group of automorphisms. In general, the self-adjoint generator is not localized.  Is disputable if it belongs to the representation of the algebra of observables. In certain cases it should be, think of the Hamiltonian with respect to some time evolution.