Interacting tachyon Fermi gas
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.