We rigorously prove that, in any relativistic kinetic theory whose nonhydrodynamic sector has a finite gap, the Taylor series of all hydrodynamic dispersion relations has a finite radius of convergence. Furthermore, we prove that, for shear waves, such radius of convergence cannot be smaller than 1/2 times the gap size. Finally, we prove that the nonhydrodynamic sector is gapped whenever the total scattering cross section (expressed as a function of the energy) is bounded below by a positive nonzero constant. These results, combined with well-established covariant stability criteria, allow us to derive a rigorous upper bound on the shear viscosity of relativistic dilute gases.

中文翻译：

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相对论动力学理论中流体动力学梯度扩展的收敛


我们严格证明，在任何非流体动力学扇区具有有限间隙的相对论动力学理论中，所有流体动力学分散关系的泰勒级数都具有有限的收敛半径。此外，我们证明，对于横波，这种收敛半径不能小于间隙大小的 1/2 倍。最后，我们证明，每当总散射截面（表示为能量的函数）在下面以正非零常数为界时，非流体动力学扇区就会出现间隙。这些结果，结合成熟的协变稳定性准则，使我们能够推导出相对论性稀气体剪切粘度的严格上限。