The Sine-Gordon QFT in de Sitter spacetime

Understand

We consider the massless Sine-Gordon model in de Sitter spacetime, in the regime $\beta^2 < 4 \pi$ and using the framework of perturbative algebraic quantum field theory.

• We show that a Fock space representation exists for the free massless field, but that the natural one-parameter family of vacuum-like states breaks the de Sitter boost symmetries.
• We prove convergence of the perturbative series for the S matrix in this representation, and construct the interacting Haag-Kastler net of local algebras from the relative S matrices.
• We show that the net fulfills isotony, locality and de Sitter covariance (in the algebraic adiabatic limit), even though the states that we consider are not invariant.