Based on the functional formalism for perturbative Algebraic Quantum Field Theory, the Haag-Kastler net of local von Neumann algebras is constructed in the ultraviolet finite regime of the sine-Gordon model. This gives an example of a theory satisfying the Haag-Kastler axioms. The approach does not need an auxiliary mass nor the detour of Euclidean signature.
This is joint work with Kasia Rejzner and Klaus Fredenhagen.
Fabien Vignes-Tourneret