Scattering in a Finite, Minkowski 1$+$1D Lattice

There has been recent developments to allow lattice calculations in Minkowski space-time in order to determine real-time observables. These still require the use of finite volumes, where scattering observables may not be accessed directly. Furthermore, it is not obvious how one can recover infinite-volume scattering amplitudes from finite-volume Minkowski observables. To address this issue, we introduce a physical quantity that can be accessed from finite-volume Minkowski correlates and smoothly recovers the two-particle amplitude in the infinite volume limit. We test the convergence of this idea by considering a strongly interacting 1$+$1D toy model.