In this work we study the effects of the electromagnetic coupling in natural inflation in a systematic manner using the Schwinger-Keldysh formalism. The corresponding influence functional is evaluated to one-loop level. It can be interpreted as due to a single stochastic force. The equation of motion of the inflaton field is therefore given in the form of a Langevin equation. Lastly, the two-point and the three-point correlation functions of the inflaton field are worked out. They are related to the power spectrum and the nongaussianity of the inflaton field, respectively.

中文翻译：

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自然膨胀中的电磁耦合效应

在这项工作中，我们使用 Schwinger-Keldysh 形式主义系统地研究了电磁耦合对自然暴胀的影响。相应的影响函数被评估为一个循环级别。它可以解释为由于单一的随机力。因此，暴胀子场的运动方程以朗之万方程的形式给出。最后，计算了暴胀子场的两点和三点相关函数。它们分别与暴胀子场的功率谱和非高斯性有关。