Toda theories as contraction of affine Toda theories

TL;DR

This paper demonstrates how Toda theories can be derived as contractions of affine Toda theories, revealing their structures and dependencies, including equations of motion, Lax pairs, boundary terms, and transfer matrices.

Contribution

It introduces a contraction method to obtain Toda theories from affine Toda theories, detailing their classical and quantum structures.

Findings

Derived Toda theories from affine Toda theories via contraction.

Established the dependence of Lax pairs and transfer matrices on spectral parameters.

Provided explicit structures for boundary terms and quantum transfer matrices.

Abstract

Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half line theories, and the quantum transfer matrix. The Lax pair and the transfer matrix so obtained, depend nontrivially on the spectral parameter.