The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalization in perturbation theory. We show, however, that exact renormalization reveals a rich nonperturbative structure, and that the model provides a physical example of a theory with a chaotic coupling trajectory and multivalued $\beta$ function. We also construct an exact Wilsonian-like renormalization group flow for the effective scattering matrix, and show how multivalued features arise in the flow. Our results shed light on nonperturbative aspects of renormalization and on the structure of the Jaynes-Cummings model itself.

中文翻译：

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Jaynes-Cummings模型的重整化组流

Jaynes-Cummings模型是光与物质相互作用的基石。虽然有限，但该模型提供了扰动理论中重新规范化的一个示例。但是，我们表明，精确的重归一化揭示了丰富的非扰动结构，并且该模型提供了具有混沌耦合轨迹和多值理论的物理示例。$\beta$功能。我们还为有效散射矩阵构造了一个精确的类似于Wilsonian的重归一化组流，并显示了多值特征如何在流中产生。我们的结果揭示了重新归一化的非扰动方面以及Jaynes-Cummings模型本身的结构。