Local quantum physics

This is the Haag-Kastler framework for quantum field theory, also known as AQFT.

Let Mink be the category of open subsets of Minkowski space with inclusions as morphisms. We have a covariant functor from Mink to uC*alg, the category of unital C* algebras such that every morphism in Mink maps to a monomorphism in uC*alg (isotony). The Poincaré group acts continuously on Mink. There exists a pullback of this action, which is continuous in the norm topology of (Poincaré covariance). Minkowski space has a causal structure. If an open set V lies in the causal complement of an open set U, then the image of the maps and commute (spacelike commutativity). If is the causal completion of an open set U, then is an isomorphism (primitive causality).

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