For ε²<4π the λsin(εΦ+θ) quantum field model corresponding to the "sine-Gordon" equation with a nonvanishing mass term in two space-time dimensions exists and yields a field theory satisfying the Wightman axioms. For |λ| small enough, the Euclidean Green's functions of this model have a convergent Feynman perturbation series. For λ large enough and positive, ε positive, and θ=0, the Φ→-Φ symmetry is presumably dynamically broken.
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Jürg Fröhlich (1975) studied this question.
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