Tachyonic Dirac sea

Abstract

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.