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

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.