Tachyonic Dirac sea
  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.
