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Local nets of von Neumann algebras in the sine-Gordon model. (English) Zbl 07333675
Summary: 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.
MSC:
81T05 Axiomatic quantum field theory; operator algebras
35Q55 NLS equations (nonlinear Schrödinger equations)
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T08 Constructive quantum field theory
81U20 \(S\)-matrix theory, etc. in quantum theory
46L05 General theory of \(C^*\)-algebras
46L10 General theory of von Neumann algebras
46L60 Applications of selfadjoint operator algebras to physics
46L30 States of selfadjoint operator algebras
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