Local quantum field theory

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. Because of this it is 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 ${\displaystyle {\mathcal {A}}}$ 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 ${\displaystyle {\mathcal {A}}(M)}$ (Poincaré covariance).

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