标题： 重新审视随机膨胀的拉格朗日公式化 显示英文标题

标题： Revisiting Lagrangian Formulation of Stochastic inflation

摘要： 我们重新审视随机暴胀的拉格朗日表述，其中采用路径积分方法推导出描述长波长场动力学的郎之万方程，这与标准方法不同，标准方法是直接从全量子场的运动方程推导出郎之万方程。 专注于一个在德西特背景下的无质量、最小耦合标量场，具有四次自相互作用，我们重新推导出影响泛函的形式表达式，该泛函在耦合常数的二阶精度下包含了短波长场的影响，并将我们的结果与早期工作中得到的结果进行比较。 在此过程中，我们强调了一些之前被忽视的细节，包括长波长和短波长模态之间的非正交性，我们对此进行了详细分析，以及在影响泛函的虚部中处理一般相互作用项缺乏一致的方案。 后一个问题指出了一个更广泛的挑战：缺乏一种普遍接受的框架来处理有效作用量的虚部。 显示英文摘要

摘要： We revisit the Lagrangian formulation of stochastic inflation, where the path-integral approach is employed to derive the Langevin equation governing the dynamics of long-wavelength fields, in contrast to the standard method where the Langevin equation is derived directly from the equation of motion of the full quantum field. Focusing on a massless, minimally coupled scalar field with quartic self-interaction in a de Sitter background, we re-derive the formal expression for the influence functional that encapsulates the effects of short-wavelength fields up to second order in the coupling constant, and compare our results with those obtained in earlier works. In doing so, we highlight certain subtleties that have been previously overlooked, including the non-orthogonality between long- and short-wavelength modes, which we analyze in detail, as well as the absence of a consistent prescription for handling general interaction terms in the imaginary part of the influence functional. The latter issue points to a broader challenge: the lack of a universally accepted framework for treating the imaginary component of effective actions.