用于推导非相对论有效场论的广义Foldy-Wouthuysen方法
Generalized Foldy-Wouthuysen approach for the derivation of non-relativistic effective field theories
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中文总结 AI 辅助
本研究提出一种基于扩展Foldy-Wouthuysen变换的广义非相对论约化方法，可推导非相对论有效场论，适用于惯性及非惯性时空等复杂理论场景，还可扩展至含轴子场的模型。
中文摘要 AI 辅助
有效场论（EFTs）是一种强大的框架，相较于其基础对应理论，可在降低复杂度的同时实现高精度计算。非相对论（NR）领域的EFTs是其中一类尤为重要的理论，其构建依赖于基础对称性的不同实现方式，因为在非相对论领域，洛伦兹不变性不再以协变形式显现。这种特性在某些匹配系数之间建立了关联，进而产生额外约束，通常被称为隐藏洛伦兹不变性。这些约束是在惯性平直时空的量子场论（如NR量子电动力学）中确立的，但对于包含超出标准模型的物理或在非惯性时空背景下构建的理论，推导这些约束会变得复杂得多，因为其隐藏对称性结构不够清晰。本研究提出一种方法，通过先构建相对论EFT，再基于扩展的Foldy-Wouthuysen变换执行广义非相对论约化，从而获得NR EFT。我们以惯性平直时空下描述电磁和强相互作用的量子色动力学EFT为例阐释该方法，展示其如何约化为已确立的NR量子色动力学与电动力学拉格朗日量，而隐藏洛伦兹不变性是该构建的直接结果。该方法为获取更复杂理论的非相对论极限提供了途径，例如非惯性时空中的狄拉克场或包含超出标准模型物理的扩展理论。作为示例，我们将该方法应用于在简化模型中添加赝标量轴子场的耦合，并推导其非相对论极限。
英文摘要
Effective field theories (EFTs) are a powerful framework for performing high-precision calculations at reduced complexity compared to their fundamental counterparts. A particularly important class of EFTs arises in the non-relativistic (NR) regime. Their construction relies on a different realization of the underlying symmetries, since Lorentz invariance is no longer manifest in covariant form in the NR regime. This behavior imposes a link between certain matching coefficients, and therefore additional constraints, commonly referred to as hidden Lorentz invariance. These constraints are established in quantum field theories on inertial flat spacetime, such as NR quantum electrodynamics. However, deriving these constraints becomes considerably more involved for theories involving physics beyond the Standard Model or formulated in non-inertial spacetime backgrounds, where the hidden symmetry structure is less transparent. In this work, we present an approach to obtain the NR EFT by first constructing a relativistic EFT and then performing a generalized NR reduction based on an extended Foldy-Wouthuysen transformation. We illustrate this method by a quantum chromo-electrodynamics EFT for inertial flat spacetime, describing both electromagnetic and strong interactions, and show how it reduces to the established Lagrangian of NR quantum chromodynamics and electrodynamics. The hidden Lorentz invariance emerges as a direct consequence of the construction. This approach provides a route to obtain the NR limits of more complex theories, \eg Dirac fields in non-inertial spacetime or extensions involving physics beyond the Standard Model. As an example, we apply the method to add the coupling of a pseudoscalar axion field in a simplified model and derive its NR limit.
发表机构
- Yokohama National University（横滨国立大学）
- Universität Ulm（乌尔姆大学）
- Technische Universität Darmstadt（达姆施塔特工业大学）
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