City Research Online

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

Fring, A., Korff, C. and Schulz, B. J. (1999). The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory. Nuclear Physics B, 549(3), pp. 579-612. doi: 10.1016/S0550-3213(99)00216-3

Abstract

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA-equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA-equations allows to derive the related Y-systems and a reformulation of the equations into a universal form.

Publication Type: Article
Additional Information: 37 pp Latex, 5 figures
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Related URLs:
URI: http://openaccess.city.ac.uk/id/eprint/947
[img] PDF
Download (436kB)

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login