This paper addresses the treatment of total time derivative interactions in the in-in perturbation theory, which is crucial for calculating primordial correlation functions in inflationary cosmology. The authors highlight the conceptual and technical challenges associated with these interactions, which are often incorrectly treated as "boundary terms." They demonstrate that total time derivatives and terms proportional to the linear equations of motion can lead to large contributions that cancel at different orders in the perturbation series. The paper discusses the Lagrangian path integral formulation and introduces a new method using canonical transformations to simplify interactions in the Hamiltonian, avoiding the need for integrations by parts. This approach is applied to single-field inflation, showing how it simplifies the calculation of correlation functions and avoids the generation of total time derivatives. The authors provide explicit results for cubic interactions in single-field inflation, including scalar and tensor sectors, and discuss the implications for quartic interactions. The paper concludes with a summary of the main findings and directions for future research.This paper addresses the treatment of total time derivative interactions in the in-in perturbation theory, which is crucial for calculating primordial correlation functions in inflationary cosmology. The authors highlight the conceptual and technical challenges associated with these interactions, which are often incorrectly treated as "boundary terms." They demonstrate that total time derivatives and terms proportional to the linear equations of motion can lead to large contributions that cancel at different orders in the perturbation series. The paper discusses the Lagrangian path integral formulation and introduces a new method using canonical transformations to simplify interactions in the Hamiltonian, avoiding the need for integrations by parts. This approach is applied to single-field inflation, showing how it simplifies the calculation of correlation functions and avoids the generation of total time derivatives. The authors provide explicit results for cubic interactions in single-field inflation, including scalar and tensor sectors, and discuss the implications for quartic interactions. The paper concludes with a summary of the main findings and directions for future research.