Local Nets of Von Neumann Algebras in the Sine–Gordon Model

The Haag–Kastler net of local von Neumann algebras is constructed in the ultraviolet finite regime of the Sine–Gordon model, and its equivalence with the massive Thirring model is proved. In contrast to other authors, we do not add an auxiliary mass term, and we work completely in Lorentzian signature. The construction is based on the functional formalism for perturbative Algebraic Quantum Field Theory together with estimates originally derived within Constructive Quantum Field Theory and adapted to Lorentzian signature. The paper extends previous work by two of us.