旋转膨胀宇宙中慢子和快子的稳定性
Stability of tardyons and tachyons in the rotating and expanding Universe
摘要：
本文分析了在膨胀和旋转的宇宙学背景下，考虑缓子质量（$μ^2 >0$）和快子质量（$μ^2 <0$）的大质量标量场和狄拉克场的准正规模谱。所发现的光谱显示出许多在闵可夫斯基时空中不存在的奇特特征。一种假设的粒子，运动速度超过光速，\emph{a tachyon}，在闵可夫斯基时空中是经典不稳定的。这种不稳定性在量子水平上也有类似的情况：场的小真空涨落导致振幅的无限增长，因此，在光谱中出现真实的快子意味着理论中存在灾难性的不稳定性。很久以前就已经证明，质量不为零的最轻粒子中微子可能是快子。在这里，我们将证明，在旋转和膨胀的宇宙中，快子是稳定的，如果它们的质量小于某个常数，这与宇宙的旋转和膨胀尺度有关。目前的旋转尺度的上限给了我们一个非常小的快子质量的上限，它比电子的质量小很多个数量级，这也许可以解释为什么只有非常轻的粒子才有机会成为快子。结果表明，“正常”（$μ^2 >0$）狄拉克场的频谱作为波矢$k_z$在$k_z = 0$的z分量的函数具有不连续性。关键词：OPERA，超光速中微子。
英文摘要：
In the present paper we analyze the spectrum of quasinormal modes for massive scalar and Dirac fields, allowing for both tardyonic ($μ^2 >0$) and tachyonic ($μ^2 <0$) masses, in the expanding and rotating cosmological background. The spectrum found shows a number of peculiar features, which are absent in the Minkowski space-time. A hypothetical particle that moves faster than light, \emph{a tachyon}, is known to be classically unstable in the Minkowski space-time. This instability has its analog at the quantum level: small vacuum fluctuations of the field lead to the unbounded growth of the amplitude, so that the appearance of the real tachyons in the spectrum means that there is catastrophic instability in the theory. It has been conjectured a long time ago that possibly the lightest particles with nonzero mass, the neutrino, may be a tachyon. Here we shall show that in the rotating and expanding Universe tachyons are stable if their mass is less than some constant, which is related to the Universe's rotation and expansion scales. The current upper bound on the rotation scale gives us a very small upper bound on the tachyon's mass which is many orders less than the mass of the electron. This might explain why only very light particles have the chance of becoming tachyons. It is shown that the spectrum of the "normal" ($μ^2 >0$) Dirac field has a discontinuity as a function of the z-component of the wave vector $k_z$ at $k_z = 0$. Keywords: OPERA, superluminal neutrino.
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