Haag–Kastler axioms

Summary

The Haag–Kastler axioms describe a relativistic quantum field theory by a net of C*-algebras. The net gives one algebra of observables for each bounded region of Minkowski space. The axioms ask for isotony, locality, covariance under the Poincaré group and a vacuum state with positive energy. They are the base of algebraic quantum field theory, which studies quantum field theory without fields, using only local observables. Many structural results, such as the Reeh–Schlieder theorem, can be stated and proved in this frame.