Local Algebra requirement

[SachaAmiel]

Amongst the requirements of an AQFT on $\mathbb{M}$ is the here-above sub-algebra requirement...

I am surprised we do not ask for a -subalbegra (one cold imagine a sub algebra not closed by ) The same requirement could be asked about in the C case, but that could be a much less physical issue as the C constraints seems a lot more like an "easyness" constraint than an actually physical constraint (just like working with $\mathcal{B}(H)$ is not verified by all QMs...)

[SachaAmiel]

Note: this detail might become more important once we work on any Lorenzian space...

[SachaAmiel]

As it turns out, this is really not a big deal, as they point out, 3 pages later, that in practice, they will require all local algebras $\mathcal{A}(\mathcal{O})$ to be C*... So I guess I will just ask the supervisor, what she thinks is truly physical, but not worry about it too much...