Quantized "Sine-Gordon" Equation with a Nonvanishing Mass Term in Two Space-Time Dimensions

Abstract

For ${\epsilon }^2<4\mathrm{}\pi$ the $\lambda sin(\epsilon \Phi +\theta )$ 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 $\left|\lambda \right|$ small enough, the Euclidean Green's functions of this model have a convergent Feynman perturbation series. For $\lambda$ large enough and positive, $\epsilon$ positive, and $\theta =0\mathrm{}$, the $\Phi \to -\Phi$ symmetry is presumably dynamically broken.