  We consider supersymmetry field theory with supercomponents being the square
root of the Bose condensate density, the amplitude of its fluctuations and
Grassmannian fields related to the Fermi particles density. The fermion number
is demonstrated to be conserved in degenerated Fermi-Bose mixtures with
unbroken supersymmetry when the system is invariant with respect to inversion
of the time arrow. We show the supersymmetry breaking allows one to derive
field equations describing behavior of real Bose-Fermi mixtures. Solution of
related field equations reveals the cooling of homogeneously distributed
fermions gives first spontaneous rise to strong inhomogeneous fluctuations,
while the Bose condensate appears at a lower temperature dependent of the
fermion density.
