On an integrable discretization of the massive Thirring model in light-cone coordinates and the associated Yang-Baxter map

TL;DR

The paper develops a fully discrete, integrable discretization of the massive Thirring model (MTM) in light-cone coordinates by constructing a discrete Lax pair inspired by binary Bäcklund–Darboux transformations. It derives the fully discrete equations of motion, demonstrates reductions to scalar and Hermitian MTM, and shows how semi-discrete and continuous limits recover known MTM dynamics. A binary BD transformation is formulated for the discrete MTM, enabling explicit solutions such as a one-soliton, and symmetry properties of the Lax matrices are used to derive a parameter-dependent Yang–Baxter map with a continuous limit. The resulting YB map is explicitly constructed, shown to satisfy the parametric YBE, and admits reductions to simpler scalar forms, linking the discretization to the matrix Chen–Lee–Liu hierarchy and suggesting connections to the matrix modified KP equation.

Abstract

We propose a fully discrete analog of the massive Thirring model in light-cone coordinates by constructing its Lax-pair representation. This Lax-pair representation can also be used to define a new Yang-Baxter map, so we obtain a Yang-Baxter map that admits a continuous limit. We present most of the results for the general case where the dependent variables are matrix-valued.