  In this Letter we report exact results on the infrared asymptotics of
one-particle dynamical correlation function of the gas of impenetrable spin 1/2
fermions at infinitesimal temperature. The correlation function shows signs of
spin-charge separation with scaling behavior in the charge part and exponential
decay as a function of the space coordinate in the spin part. Surprisingly, the
anomalous dimensions in the charge part do not correspond to any unitary
conformal field theory. We find that the fermion spectral weight has a power
law divergency at low energy with the anomalous exponent $-1/2.$
