The ultraviolet behaviour of integrable quantum field theories,affine Toda field theory |
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| Affiliation: | 1. Department of Mathematics and Statistics, Swarthmore College, 500 College Avenue, Swarthmore, PA 19081, USA;1. Nanobiotechnology Laboratory, Department of Biotechnology, Bannari Amman Institute of Technology, Sathyamangalam, Tamil Nadu, India;2. Department of Botany and Microbiology, College of Science, King Saud University, Riyadh 11451, Saudi Arabia;3. Central Laboratory, Department of Pharmaceutical Chemistry, College of Pharmacy King Saud University, Riyadh, Saudi Arabia;4. Integrated Molecular Plant Physiology Research, Department of Biology, University of Antwerp, 2020 Antwerpen, Belgium;5. Department of Zoology, Mar Ivanios College, Nalanchira, Thiruvananthapuram, India;6. Department of Botany and Biotechnology, St Xavier’s College, Thumba, Thiruvananthapuram, India;1. Dept. of Electrical and Computer Engineering, University of Dayton, Dayton, OH 45469, USA;2. Department of Earth and Atmospheric Sciences, Saint Louis University, St. Louis, MO 63108, USA;1. Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan;2. Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, D-13353 Berlin, Germany |
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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 one to derive the related Y-systems and a reformulation of the equations into a universal form. |
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