The Quantum Sine Gordon model in perturbative AQFT

Abstract

We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation value - with respect to the vacuum or a Hadamard state - of the Epstein Glaser S-matrix and the interacting current or the field respectively, both given as formal power series, converge.

23 pages, in this version we computed our main estimate in a class of Hadamard states, instead of a singular state from the previous version

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