When gravitational waves travel from their source to an observer, they interact with matter structures along their path, causing distinct deformations in their waveforms. In this study we introduce a novel theoretical framework for wave optics effects in gravitational lensing, addressing the limitations of existing approaches. We achieve this by incorporating the proper time technique, typically used in field theory studies, into gravitational lensing. This approach allows us to extend the standard formalism beyond the eikonal and paraxial approximations, which are traditionally assumed, and to account for polarization effects, which are typically neglected in the literature. We demonstrate that our method provides a robust generalization of conventional approaches, including them as special cases. Our findings enhance our understanding of gravitational wave propagation, which is crucial for accurately interpreting gravitational wave observations and extracting unbiased information about the lenses from the gravitational wave waveforms.

中文翻译：

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引力波的正确时间路径积分：一种改进的波动光学框架


当引力波从其源传播到观察者时，它们会沿其路径与物质结构相互作用，从而导致其波形发生明显的变形。在这项研究中，我们引入了引力透镜中波动光学效应的新理论框架，解决了现有方法的局限性。我们通过将场论研究中常用的适当时间技术整合到引力透镜中来实现这一目标。这种方法使我们能够将标准形式扩展到传统假设的 eikonal 和 paraaxial 近似之外，并解释文献中通常被忽视的极化效应。我们证明了我们的方法提供了传统方法的稳健泛化，包括它们作为特殊情况。我们的发现增强了我们对引力波传播的理解，这对于准确解释引力波观测和从引力波波形中提取有关透镜的无偏信息至关重要。