AI 中文总结
研究量子引力中电磁波色散关系，通过扩展玻恩-奥本海默近似构建通用框架，得出准唯象模型，能自然再现色散效应。以平面量子弗里德曼-勒梅特-罗伯逊-沃克背景为例，结合多种方法提取可观测特征，该模型在全能量范围有效，能获量子引力修正。
AI 中文摘要
对电磁波色散关系的修正，是探寻量子引力效应的核心手段。本文利用扩展的玻恩-奥本海默近似，构建了电磁场与量子背景几何相互作用的通用框架，得出弯曲时空中电磁波传播的准唯象模型。与以往半经典方法不同，该框架自然再现了类似于非线性光学中光与物质相互作用的色散效应。作为具体应用，通过解析技术与数值模拟相结合，分析了平面量子弗里德曼-勒梅特-罗伯逊-沃克背景下电磁波的传播，提取了量子光与几何相互作用诱导的类似棱镜行为的可观测特征。该模型在所有能量范围均有效，能获取超出半经典极限的量子引力修正。
英文摘要
Modifications to the dispersion relation of electromagnetic (EM) waves are a central probe in the search for quantum gravitational effects. In this work, we construct a general framework for the interaction between the EM field and a quantum background geometry, employing an extended Born-Oppenheimer approximation. This leads to a quasi-phenomenological model for EM wave propagation in curved spacetime. Unlike previous semi-classical approaches for mode-dependent dispersion relations, our framework naturally reproduces chromatic dispersion effects analogous to those observed in light-matter interactions in nonlinear optics. As a concrete application, we analyze EM wave propagation on a flat quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) background, combining analytical techniques with numerical simulations to extract observable signatures of the prism-like behavior induced by quantum light-geometry interactions. Crucially, it remains valid across all energy regimes, enabling access to quantum gravitational corrections beyond the semi-classical limit.
Comments7 pages, 6 figures, references and template has been updated
