AI 中文总结
研究具有纯弛豫激发谱的相对论理论，赋予色散平面洛伦兹几何结构，通过因果性约束色散关系，将相对论物质物理问题转化为几何问题，并推导了如色散关系约束等一系列应用结果。
AI 中文摘要
我们表明，具有纯弛豫激发谱的相对论理论，如动力学理论和瞬态流体动力学，自然地赋予色散平面$\{i\omega,ik\}$一种类似于闵可夫斯基平面$\{t,x\}$的洛伦兹几何结构。在此图景中，类时未来指向、类时过去指向和类空方向分别对应于弛豫类、不稳定类和消逝类模式。在对基础理论的适度结构假设下，因果性将色散关系限制为在平面上遵循类空轨迹。这种几何观点将相对论物质物理学中的长期问题重塑为通常可通过图形解决的基本几何问题。作为应用，我们推导出色散关系的通用约束、与时间膨胀的偏差、光谱层次的观察者依赖性、流体动力学在推进框架中的有效性范围、相对论介质的最大允许扩散率和粘度，以及动力学理论中存在的非流体动力学分支切割。
英文摘要
We show that relativistic theories with purely relaxational excitation spectra, such as kinetic theory and transient hydrodynamics, naturally endow the dispersion plane $\{iω,ik\}$ with a Lorentzian geometric structure analogous to that of the Minkowski plane $\{t,x\}$. In this picture, timelike future-directed, timelike past-directed, and spacelike directions correspond respectively to relaxation-like, unstable-like, and evanescent-like modes. Under mild structural assumptions on the underlying theory, causality constrains dispersion relations to follow spacelike trajectories on the plane. This geometric viewpoint recasts longstanding problems in relativistic matter physics as elementary geometric ones that can often be solved graphically. As applications, we derive universal constraints on dispersion relations, deviations from time dilation, the observer dependence of spectral hierarchies, the regime of validity of hydrodynamics in boosted frame, the maximal allowed diffusivity and viscosity of relativistic media, and the presence of non-hydrodynamic branch cuts in kinetic theory.
Comments24 pages, 12 figures, comments welcome!
