In AQFT one specifies the structure of the observables as a $C^*$-algebra. This seems to excludes algebras that don't have a norm, such as the Heisenberg algebra. Fortunately for this case one turns to Weyl algebra.
Is that trick always possible?
Additional material:
Related to this Phys.SE post.
In Haag's book "Local quantum physics" p.5, he says that one can always come down to the study of bounded operators as discussed in I.E. Segal "Postulate for general quantum mechanics" 1947. However I don't see the answer to that question in this paper.
It seems that from an self adjoint operator in a Hilbert space one can always define a unitary operator, Reed & Simon Thm VIII.7.
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