AI 中文总结
该研究将洛伦兹协变弛豫界框架扩展到热量子场论全量子设定，通过处理推迟两点函数，利用谱函数性质及相关条件得出约束，在全息理论中验证，为夸克 - 胶子等离子体等提供了洛伦兹协变谱约束的第一性原理推导。
AI 中文摘要
我们将线性化经典动力学和流变学理论中最近建立的洛伦兹协变弛豫界框架扩展到热量子场论（QFT）的全量子设定。直接处理有限温度和密度下的推迟两点函数，我们表明谱函数的解析性和正性属性，结合洛伦兹协变性和久保 - 马丁 - 施温格（KMS）条件，对复频率平面中奇点的位置施加了严格的依赖框架的约束。具体而言，我们证明在任何推进框架中的非流体动力学准正则谱局限于一个条带，其宽度仅由零空间动量下的静止框架谱权重和理论的最大群速度决定。我们推导了洛伦兹推进下谱密度的协变和规则，并确定流体动力学梯度展开的收敛半径以由相同静止框架数据决定的方式变换。在渐近反德西特时空中与爱因斯坦引力对偶的全息理论中，我们通过显式的准正则模计算验证了这些界：主导的推进极点向复平面深处移动——观察到的弛豫率随推进速度增加，这与朴素的时间膨胀形成鲜明对比——同时始终遵守该界；我们进一步推导了来自高阶导数引力项的修正。我们的结果为适用于夸克 - 胶子等离子体、中子星物质的超流相以及量子临界点附近强关联电子的洛伦兹协变谱约束提供了第一性原理、非微扰的推导。
英文摘要
We extend the recently established framework of Lorentz-covariant relaxation bounds from linearized classical kinetic and rheological theories to the full quantum setting of thermal quantum field theory (QFT). Working directly with retarded two-point functions at finite temperature and density, we show that the analyticity and positivity properties of spectral functions -- combined with Lorentz covariance and the Kubo--Martin--Schwinger (KMS) condition -- impose rigorous frame-dependent constraints on the location of singularities in the complex frequency plane. Specifically, we prove that the non-hydrodynamic quasinormal spectrum in any boosted frame is confined to a strip whose width is determined solely by the rest-frame spectral weight at zero spatial momentum and the maximal group velocity of the theory. We derive covariant sum rules for the spectral density under Lorentz boosts and establish that the convergence radius of the hydrodynamic gradient expansion transforms in a manner dictated by the same rest-frame data. In holographic theories dual to Einstein gravity in asymptotically anti-de Sitter spacetime, we verify the bounds by an explicit quasinormal-mode computation: the leading boosted pole moves deeper into the complex plane -- the observed relaxation rate increases with boost velocity, in sharp contrast to naive time dilation -- while respecting the bound throughout; we further derive corrections from higher-derivative gravitational terms. Our results provide a first-principles, non-perturbative derivation of Lorentz-covariant spectral constraints applicable to the quark-gluon plasma, superfluid phases of neutron star matter, and strongly correlated electrons near quantum critical points.
