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The structure of a new family of factorised $S$-matrix theories with resonance poles is reviewed. They are conjectured to correspond to the Homogeneous sine-Gordon theories associated with simply laced compact Lie groups. Two of their more remarkable properties are, first, that some of the resonance poles can be traced to the presence of unstable particles in the spectrum, and, second, that they involve several independent mass scales. The conjectured relationship with the simply laced HSG theories has been checked by means of the Thermodynamic Bethe ansatz (TBA) and, more recently, through the explicit calculation of the Form Factors. The main results of the TBA analysis are summarized.
We determine the semiclassical energy levels for the phi^4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite--volume kink solutions. The analytic form of
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