  We revisit the properties of total time-derivative terms as well as terms
proportional to the free equation of motion (EOM) in a Schwinger-Keldysh
formalism. They are relevant to the correct calculation of correlation
functions of curvature perturbations in the context of inflationary Universe.
We show that these two contributions to the action play different roles in the
operator or the path-integral formalism, but they give the same correlation
functions as each other. As a concrete example, we confirm that the Maldacena's
consistency relations for the three-point correlation function in the slow-roll
inflationary scenario driven by a minimally coupled canonical scalar field hold
in both the operator and path-integral formalisms. We also give some comments
on loop calculations.
