  We consider a system of many fermionic tachyons coupled to a scalar,
pseudoscalar, vector and pseudovector fields. The scalar and pseudoscalar
fields are responsible for the effective mass, while the pseudovector field is
similar to ordinary electromagnetic field. The action of vector field
$\omega_\mu$ results in tachyonic dispersion relation
$\varepsilon_p=\sqrt{p^2+g^2\omega_0^2-hpg\omega_0-g\vec \sigma \cdot \nabla
\omega_0-m^2} -g\vec \sigma \cdot \vec \omega$ that depends on helicity $h$ and
spin $\vec \sigma$. We apply the mean field approximation and find that there
appears a vector condensate with finite average $<\omega_0>$ depending on the
tachyon density. The pressure and energy density of a many-tachyon system
include the mean-field energy $<\varepsilon_p>
=\sqrt{p^2+hpng^2/M^2+n^2g^4/M^4-m^2}$ which is real when the particle number
density exceeds definite threshold which is $n>mM^2/g^2$ for right-handed and
$n>\frac 2{\sqrt{3}}mM^2/g^2$ for left-handed tachyons, while all tachyons are
subluminal at high density. There is visible difference in the properties of
right-handed and left-handed tachyons. Interaction via the vector field
$\omega_0$ may lead to stabilization of tachyon matter if its density is large
enough.
