Integrable semi-discretization of the massive Thirring system in laboratory coordinates

Several integrable semi-discretizations are known in the literature for the massive Thirring system in characteristic coordinates. We present for the first time an integrable semi-discretization of the massive Thirring system in laboratory coordinates. Our approach relies on the relation between the continuous massive Thirring system and the Ablowitz–Ladik lattice. In particular, we derive the Lax pair for the integrable semi-discretization of the massive Thirring system by combining together the time evolution of the massive Thirring system in laboratory coordinates and the Bäcklund transformation for solutions to the Ablowitz–Ladik lattice.