发表机构
INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所格兰萨索国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过分析耦合正常与鬼子系统模型的准基态时间演化，发现其在广泛耦合范围内不衰变且长期稳定，为解决负能量鬼态导致的哈密顿量无下界稳定性问题提供了证据。
AI 中文摘要
许多量子场论模型，无论是通过高阶导数项来改善紫外行为，还是旨在提供引力的统一描述，都不可避免地引入负能量的“鬼”态。这些态引发了关于理论稳定性的根本性问题。在本研究中，我们探究了由两个耦合的正常子系统和鬼子系统组成的简化量子力学模型的时间演化。尽管这些模型的完整谱从下方无界，因此缺乏真正的基态，我们聚焦于“准基态”的时间演化：即解耦系统的零能量本征态。通过分析其在相互作用下的亚稳定性，我们获得了对鬼态动力学行为的见解。与标准范式相反，我们的结果表明，在广泛的耦合范围内，准基态不会衰变，并在长时间内保持动力学稳定。这为解决从下方无界的哈密顿量的稳定性问题提供了证据。我们还讨论了与相应经典和半经典动力学的联系。
英文摘要
Many Quantum Field Theory models, either designed to improve the ultraviolet behavior via higher derivative terms or aimed at providing unified descriptions of Gravity, inevitably introduce negative-energy 'ghosts' states. These states raise fundamental questions regarding the stability of the theory. In this study, we investigate the time evolution of simplified quantum mechanical models consisting of two coupled normal and ghost subsystems. Although the full spectrum of these models is unbounded from below and, therefore, lacks a true ground state, we focus the time evolution of a 'would-be ground state': a zero-energy eigenstate of the decoupled system. By analyzing its metastability under interactions, we gain insights into the dynamics of ghost-like states. Contrary to the standard paradigm, our results demonstrate that, across a broad range of couplings, the would-be ground state does not decay and remains dynamically stable over long times. This provides evidence towards resolving the stability problems of Hamiltonians that are unbounded from below. We also discuss the connections with the corresponding classical and semiclassical dynamics.
Comments33 pages, 22 figure
