快子狄拉克海
Tachyonic Dirac sea
摘要：
本文考虑了一个具有能谱\varepsilon_k = \sqrt{k^2-m^2}的多费米子系统，阐明了具有虚能和低动量（k<m）的快子在多快子费米系统中起着狄拉克海的作用，对系统的物理函数有贡献。能量和压力获得了额外的常数项，然而，这些常数项并没有反映在声速中。置换$m=im$得到普通费米气体的热力学函数和声速。当费米动量接近狄拉克海平面k_F=m时，大多数快子的群速度是不受约束的，而声速则趋于无穷大。这种情况在实际中不会遇到，因为当k_F< \sqrt{3/2} m时，冷快子费米气体对于流体动力学扰动变得不稳定。一个稳定的多快子系统的粒子数密度总是有限的，并超过取决于快子质量m的临界值。
英文摘要：
We consider a system of many fermions with tachyonic energy spectrum \varepsilon_k=\sqrt{k^2-m^2} and clarify that tachyons with imaginary energy and low momentum (k<m) play the role of Dirac sea in a many-tachyon Fermi system and make contribution to the thermodynamical functions. The energy and pressure acquire additional constant terms that, however, is not reflected in the sound speed. Replacement $m=im$ results in the thermodynamical functions and the sound speed of an ordinary Fermi gas. When the Fermi momentum approaches the Dirac sea level k_F=m, the group velocity of most tachyons above the sea is unbound, while the sound speed tends to infinity. This scenario is not encountered in practice because the cold tachyon Fermi gas becomes unstable with respect to hydrodynamical perturbations when k_F<\sqrt{3/2}m. The particle number density of a stable many-tachyon system is always finite and exceeds the critical value depending on the tachyon mass m.
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