伽利略子有效场论（EFT）中的非线性演化：正则化与屏蔽效应

中文摘要 AI 辅助

在具有伽利略子对称性的标量有效场论（EFT）中，我们将强场展开与导数展开区分开来，研究球对称的经典非线性动力学。具体而言，我们考虑两个通过微扰场重定义关联的模型：一个具有二阶方程且可表现出屏蔽效应，另一个包含高阶导数项，该项会引入传播鬼场；后者属于可“正则化”方程、使其作为初值问题适定的类型。对于满足导数展开的初始数据，我们发现第一个无鬼场、未正则化的模型仅在导数展开失效时，演化过程中才会出现不适定区域，该结果在强场区域依然成立。我们还发现，当未正则化模型保持适定时，正则化模型会复现其演化；而当未正则化模型变得不适定时，正则化模型会表现出快子行为。我们进一步考虑对应于未正则化无鬼理论中表现出屏蔽效应的定态的初始数据，在此情况下，对于未正则化模型出现不适定区域的初始数据，正则化理论可保持适定；但与通常预期相反，在屏蔽区域，鬼场项自然会主导伽利略子项。

英文摘要

In a scalar effective field theory (EFT) with Galileon symmetry, we distinguish the strong-field expansion from the derivative expansion and study spherically symmetric classical nonlinear dynamics. More concretely, we consider two models related via perturbative field redefinitions: one with second-order equations that can also exhibit screening, and one that includes a higher-derivative term that introduces a propagating ghost. The latter term is of the type that can ``regularise'' the equations to render them well-posed as an initial value problem. For initial data that respect the derivative expansion, we find that the first model (ghost-free, unregularised) develops ill-posed regions during evolution only when the derivative expansion breaks down. This result persists in the strong-field regime. We further find that the regularized model reproduces the evolution of the unregularised one when the latter remains well-posed, while it exhibits tachyonic behaviour when the unregularised one becomes ill-posed. We also consider initial data that corresponds to stationary states that exhibit screening in the unregularised, ghost-free theory. In this case, we find that the regularised theory can remain well-posed for initial data that the unregularised one developed ill-posed regions. However, the ghost term naturally dominates over the Galileon term in the screening regime, contrary to common expectation.

发表机构

• University of Nottingham（诺丁汉大学）
• SISSA（的里雅斯特国际高等研究学校）
• INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
• Institut de Physique Théorique Philippe Meyer, Laboratoire de Physique de l’École normale supérieure (ENS), Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎文理研究大学/法国国家科学研究中心/索邦大学/巴黎西岱大学菲利普·迈耶理论物理研究所/高等师范学校物理实验室）
• IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）

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