A quantum field theory with infinite resonance states

We study an integrable quantum field theory of a single stable particle wit h an infinite number or resonance states. The exact S-matrix of the model i s expressed in terms of Jacobian elliptic functions which encode the resona nce poles inherently. In the limit l --> 0, with l the modulus of the Jacob ian elliptic function, it reduces to the Sinh-Gordon S-matrix. We address t he problem of computing the form factors of the model by studying their mon odromy and recursive equations. These equations turn out to possess infinit ely many solutions for any given number of external particles. This infinit e spectrum of solutions may be related to the irrational nature of the unde rlying conformal field theory reached in the ultraviolet limit. We also dis cuss an elliptic version of the thermal massive Ising model which is obtain ed by a particular value of the coupling constant. (C) 2000 Elsevier Scienc e B.V. All rights reserved.