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

Fring, A., Korff, C., and Schulz, B. (1999) The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory. Nuclear Physics B, 549 (3). pp. 579-612. ISSN 0550-3213 (doi:10.1016/S0550-3213(99)00216-3)

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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.

Item Type:Article
Status:Published
Refereed:Yes
Glasgow Author(s):Korff, Dr Christian
Authors: Fring, A., Korff, C., and Schulz, B.
Subjects:Q Science > QA Mathematics
Q Science > QC Physics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Integrable Systems and Mathematical Physics
Journal Name:Nuclear Physics B
ISSN:0550-3213
Published Online:19 July 1999

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