热量子场论中的洛伦兹协变谱界
Lorentz-Covariant Spectral Bounds from Thermal Quantum Field Theory
AI总结：
该研究从热量子场论中推迟格林函数解析结构出发，利用相关条件推导出洛伦兹协变谱界，证明了能隙变换关系等，通过数值计算验证，结果适用于夸克 - 胶子等离子体等系统。
AI中文摘要：
我们直接从热量子场论中推迟格林函数的解析结构出发，仅利用因果性、幺正性、久保 - 马丁 - 施温格条件和洛伦兹协变性，推导出关于弛豫谱的严格洛伦兹协变界，无需参考任何特定动力学模型。在推进参考系中，单个静止参考系准正则极点通常会扩展为一个激发连续统，其宽度由最大信号速度设定。我们证明了非流体动力学能隙$\Gamma_{\mathrm{gap}}$的变换关系为$\tilde{\Gamma}_{\mathrm{gap}} \geq \Gamma_{\mathrm{gap}}/[\gamma(1 + v v_{\mathrm{max}})]$，并且在速度为$v$的推进下，流体动力学梯度展开的收敛半径满足$\tilde{k}_c \in [k_c/\gamma(1+v v_s), k_c/\gamma(1-v v_s)]$。我们通过在${N}=4$超杨 - 米尔斯等离子体中的数值准正则模计算验证了这些界：领先的推进极点向复平面更深处移动，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，同时始终遵循该界。结果非微扰地适用于夸克 - 胶子等离子体、中子星合并动力学和量子临界系统。
英文摘要：
We derive rigorous Lorentz-covariant bounds on relaxation spectra directly from the analytic structure of retarded Green's functions in thermal quantum field theory, using only causality, unitarity, the Kubo-Martin-Schwinger condition, and Lorentz covariance, without reference to any specific dynamical model. A single rest-frame quasinormal pole is generically smeared into a continuum of excitations in boosted frames, with width set by the maximal signal velocity. We prove that the non-hydrodynamic gap $Γ_{\mathrm{gap}}$ transforms as $\tildeΓ_{\mathrm{gap}} \geq Γ_{\mathrm{gap}}/[γ(1 + v v_{\mathrm{max}})]$, and that the convergence radius of the hydrodynamic gradient expansion satisfies $\tilde{k}_c \in [k_c/γ(1+v v_s), k_c/γ(1-v v_s)]$ under a boost of velocity $v$. We verify the bounds by a numerical quasinormal-mode computation in the ${N}=4$ super-Yang-Mills plasma: 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. The results apply non-perturbatively to the quark-gluon plasma, neutron star merger dynamics, and quantum critical systems.
