Exploring the gravitational impulse via the quantum Boltzmann equation

We investigate the gravitational impulse by using the generalized formulation of the quantum Boltzmann equation (QBE), wherein the initial states are taken as wave packets rather than plane waves. The QBE operates within an open quantum system framework. Using this approach, we can analyze the two-body gravitational scattering by considering one body as part of the environment and the other as the system. Through this procedure, we obtain the system’s impulse up to the second order for two massive objects. Similarly, we apply the forward scattering of the QBE to the gravitational impulse of a photon due to a massive object, during which we consider the photon as the system and the massive object as the environment. In this methodology, we use the QBE to compute the time evolution of the momentum operator associated with the system. While the forward scattering term vanishes when considering point particles, we demonstrate its persistence when using wave packets to describe both massive particles and the photon field. The results reported here are entirely consistent with the previous approaches.