= Algebraic quantum field theory
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<Algebraic quantum field theory> assigns an observable algebra $\mathcal A(O)$ to each suitable spacetime region $O$. Inclusion of regions implies inclusion of algebras, and spacelike-separated algebras commute under <microcausality>. A state is a positive normalized functional on the observable algebra, so its restriction to a region specifies expectation values and correlations for that algebra. <Spectrum conditions> restrict translation representations, while <primitive causality> and <time-slice axioms> constrain the dynamics; these are different assumptions.
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