Constructing infinite particle spectra - art. no. 085005

We propose a general construction principle which allows us to include an i nfinite number of resonance states into a scattering matrix of hyperbolic t ype. As a concrete realization of this mechanism we provide new S matrices generalizing a class of hyperbolic ones. which are related to a pair of sim ple Lie algebras, to the elliptic case. For specific choices of the algebra s we propose elliptic generalizations of affine Toda field theories and the homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model we compute explicitly renormalization group scaling functions by mean s of the c theorem and the thermodynamic Bethe ansatz. In particular we ide ntify the Virasoro central charges of the corresponding ultraviolet conform al field theories.