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The Haag-Kastler axiomatic framework for quantum field theory is an application to local quantum physics of C-star algebra theory. It is therefore also known as Algebraic Quantum Field Theory (AQFT). The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those.
Let Mink be the category of open subsets of Minkowski space with inclusion maps as morphisms. We are given a covariant functor <math>\mathcal{A}<math> 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 <math>\mathcal{A}(\mathbb{R}^4)<math> (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
- <math>\mathcal{A}(i_{U,U\cup V})<math>
and
- <math>\mathcal{A}(i_{V,U\cup V})<math>
commute (spacelike commutativity). If <math>\bar{U}<math> is the causal completion of an open set U, then <math>\mathcal{A}(i_{U,\bar{U}})<math> is an isomorphism (primitive causality).
External links
Local Quantum Physics Crossroads (http://www.lqp.uni-goettingen.de/)
es:Física local cuántica
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