弱相互作用与环境修饰的格林函数统一描述
A Green-function unification of weak interactions with environmental dressing
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- University of Bergen（卑尔根大学）
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中文总结 AI 辅助
本文提出统一量子电动力学框架，以电磁格林函数统一描述静电、感应和色散等弱相互作用，环境效应通过修饰格林函数引入，并恢复经典极限，使格林函数成为复杂环境中弱相互作用的普适组织原则。
中文摘要 AI 辅助
弱非共价相互作用，如静电、感应和色散作用，通常被视为不同的物理机制，并常采用各自独立的模型和近似进行处理。在此，我们提出一个统一的量子电动力学框架，其中中性或带电子系统之间的所有弱相互作用均源自单一相互作用哈密顿量，并完全以电磁格林函数来表达。从任意线性环境中的宏观QED出发，我们推导出紧凑的主公式，这些公式能够平等地生成永久静电相互作用、混合感应相互作用以及完全感应（色散）相互作用。单极子、偶极子和四极子在相同的多极展开中被一致地处理，从而得到一个共同的结构形式，其中所有相互作用通道均通过多极矩和响应函数与格林张量的缩并获得。环境效应通过修饰后的格林函数普遍地引入。标准的非延迟自由空间极限，包括Keesom、Debye和London/van der Waals相互作用，作为形式体系的一致性检验被恢复。除这一验证外，该公式表明，一旦建立了一般表达式，不同的物理场景，如界面、受限体系或可极化连续介质，均可通过直接代入相应的格林函数来处理，而无需针对每种情况重新构建相互作用。这将格林函数提升为复杂环境中弱相互作用的普适组织原则。
英文摘要
Weak, non-covalent interactions such as electrostatics, induction, and dispersion are commonly treated as distinct physical mechanisms, often using separate models and approximations. Here, we present a unified quantum-electrodynamical framework in which all weak interactions between neutral or charged subsystems emerge from a single interaction Hamiltonian and are expressed entirely in terms of electromagnetic Green functions. Starting from macroscopic QED in arbitrary linear environments, we derive compact master formulas that generate permanent electrostatic, mixed induction, and fully induced (dispersion) interactions on equal footing. Monopoles, dipoles, and quadrupoles are treated consistently within the same multipole expansion, leading to a common structural form in which all interaction channels are obtained from contractions of multipole moments and response functions with Green tensors. Environmental effects enter universally through dressed Green functions. The standard non-retarded free-space limits, including Keesom, Debye, and London/van der Waals interactions, are recovered as a consistency check of the formalism. Beyond this validation, the formulation shows that once the general expressions are established, different physical scenarios, such as interfaces, confinement, or polarisable continua, can be treated by direct substitution of the corresponding Green function, without reformulating the interaction for each case. This elevates Green functions to a universal organising principle for weak interactions in complex environments.
