发表机构
National institute of technology Calicut; University of Mumbai（国立卡利卡特理工学院; 孟买大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究κ-闵可夫斯基空间中波包的渐近行为，运用奇点理论等方法分析其衰减特性，发现其衰减率随系统控制参数变化，与交换时空存在本质差异。
AI 中文摘要
本文研究κ-闵可夫斯基空间中波包的性质及其衰减行为，分析全程采用奇点理论相关技术，具体运用拉格朗日奇点与焦散理论的方法研究能级流形的拓扑，还运用振荡积分理论中的牛顿多面体方法分析波包的衰减行为。研究发现，对于κ-闵可夫斯基空间中的一般哈密顿量，相关波包的衰减率取决于系统的控制参数：当控制参数取尖点（cusp）处的值时，衰减阶为t⁻¹/⁴；否则衰减阶为t⁻¹/²。κ-闵可夫斯基空间中波包的这种独特行为，使其与交换时空存在本质区别。
英文摘要
In this paper, we study the nature of wave packets and their decay behavior in the $κ$-Minkowski space. We employ techniques from singularity theory throughout our analysis. Specifically, we use methods from the theory of Lagrangian singularities and caustics to study the topology of the energy-level manifold. The Newton polyhedron method from the theory of oscillatory integrals is applied to analyze the decay behavior of wave packets. We find that for a generic Hamiltonian in the $κ$-Minkowski space, the associated wave packets exhibit different decay rates depending on the control parameter of the system. When the control parameter takes values on the cusp, the system exhibits decay of order $t^{-1/4}$; otherwise, it exhibits decay of order $t^{-1/2}$. This distinctive behavior of wave packets in the $κ$-Minkowski makes it fundamentally different from commutative spacetime.
