- published: 07 May 2016
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The Haag-Kastler axiomatic framework for quantum field theory, introduced by Haag and Kastler (1964), is an application to local quantum physics of C*-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 M with inclusion maps as morphisms. We are given a covariant functor Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{A}
The Poincaré group acts continuously on Mink. There exists a pullback of this action, which is continuous in the norm topology of Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{A}(M)
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 Failed to parse (Missing texvc executable; please see math/README to configure.): \bar{U}
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