Total time derivative interactions contribute to the calculations of correlation functions in the in-in formalism, as they are not merely boundary terms. Despite their importance, they have often been overlooked in the literature—most notably in Maldacena's seminal paper on Non-Gaussianities during inflation. Notably, a consistent method for their inclusion remains lacking. In this talk, I will present a systematic approach to handling total time derivative interactions within in-in perturbation theory, demonstrating the challenges they pose in both the standard operator and path integral formulations. To address these challenges, I propose a novel method for calculating primordial correlation functions that circumvents the generation of total time derivatives by working directly with the full Hamiltonian in phase-space variables. If time allows, I will showcase a few applications of this new formalism in the context of single-field inflation.