No time to derive: unraveling total time derivatives in in-in perturbation theory

Understand

The in-in formalism provides a way to systematically organize the calculation of primordial correlation functions.

• Although its theoretical foundations are now firmly settled, the treatment of total time derivative interactions, incorrectly trivialized as ``boundary terms'', has been the subject of intense discussions and conceptual mistakes.
• In this work, we demystify the use of total time derivatives -- as well as terms proportional to the linear equations of motion -- and show that they can lead to artificially large contributions cancelling at different orders of the in-in operator formalism.
• We discuss the treatment of total time derivative interactions in the Lagrangian path integral formulation of the in-in perturbation theory, and we showcase the importance of interaction terms proportional to linear equations of motion.