  The Wigner formulation of quantum mechanics is used to derive a new path
integral representation of quantum density of states. A path integral Monte
Carlo approach is developed for the numerical investigation of density of
states, internal energy and spin--resolved radial distribution functions for a
2D system of strongly correlated soft--sphere fermions. The peculiarities of
the density of states and internal energy distributions depending on the
hardness of the soft--sphere potential and particle density are investigated
and explained. In particular, at high enough densities the density of states
rapidly tends to a constant value, as for an ideal system of 2D fermions.
