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.

中文翻译：

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边界项和运动方程项在宇宙学相关函数中的作用


我们重新审视了 Schwinger-Keldysh 形式中总时间导数项以及与自由运动方程 （EOM） 成正比的项的性质。它们与在膨胀宇宙背景下正确计算曲率扰动的相关函数有关。我们表明，这两个对动作的贡献在运算符或路径积分形式中起着不同的作用，但它们彼此给出了相同的关联函数。作为一个具体的例子，我们证实了在由最小耦合规范标量场驱动的慢滚膨胀情景中，三点相关函数的 Maldacena 一致性关系在算子和路径积分形式中都成立。我们还对循环计算进行了一些评论。