Space-time-resolved Breit-Wheeler process for a model system

We study the creation process of an electron-positron pair as a result of the collision between two incoming photons with full spatial and temporal resolution. The dynamics of the four involved particles is described by a simplified model based on a Yukawa Hamiltonian in one spatial dimension. This quantum field theoretical approach permits us to go beyond the usual external field approximation and to study the depletion of the two colliding photon wave packets due to the back reaction of the created electron-positron pair. If the spatial extension of the incoming photons is sufficiently narrow, we predict an interesting blueshift with regard to the optimum incoming photon momentum that can maximize the pair-creation yield close to the threshold momentum.