The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affin e Toda field theory and whose statistical interaction is of a general Halda ne type. Up to the first leading order, we provide general approximated ana lytical expressions for the solutions of these equations from which we deri ve general formulae for the ultraviolet scaling functions for theories in w hich the underlying Lie algebra is simply laced. For several explicit model s we compare the quality of the approximated analytical solutions against t he numerical solutions, We address the question of existence and uniqueness of the solutions of the TEA equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A ge neral expression for the Fourier transformed kernels of the TEA equations a llows one to derive the related Y-systems and a reformulation of the equati ons into a universal form. (C) 1999 Elsevier Science B.V. All rights reserv ed.