  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.
