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. The Backlund transformation for solutions to the Ablowitz-Ladik lattice and the time evolution of the massive Thirring system in laboratory coordinates are combined together in the derivation of the Lax system for the integrable semi-discretization of the massive Thirring system.