Abstract:
In standard scattering theory, transition rates are calculated using plane-wave states in the long-time limit, and scattering probabilities are evaluated as the product of these rates and the scattering time. At finite times, however, contributions from temporal boundaries that cannot be expressed in this form must also be considered. In this study, we use normalized Gaussian wave packets for both the initial and final states to analyze two-body scattering probabilities in φ⁴ theory, including these boundary contributions. We focus on the interference between the zeroth-order amplitude, corresponding to propagation without scattering, and the first-order interaction amplitude. This interference contributes at a lower perturbative order than the squared first-order amplitude. In the plane-wave description, delta functions in the zeroth-order amplitude restrict the interference contribution to the exact forward direction. With wave packets, it is instead obtained as a finite function spread around the forward direction. In this presentation, I present the results of this analysis and compare the bulk and boundary contributions to the interference term. Our results show that boundary contributions also contribute to interference in the forward region and can exceed the bulk contribution under certain conditions. Finally, I briefly outline future research directions.