  By means of the continuous unitary transformation similar to a general scheme
of the Renormalization Group (RG) procedure we study the issue of symmetry
breaking and pairing instability in the system of interacting fermions.
Constructing a generalized version of the Bogoliubov transformation we show
that formation of the fermion pairs and their superconductivity/superfluidity
can appear at different temperatures. It is shown that strong quantum
fluctuations can destroy the long-range order without breaking the fermion
pairs which may still exist as incoherent and/or damped entities. Such unusual
phase is characterized by a partial suppression of the density of states near
the Fermi energy and by residual collective features like the sound-wave mode
in the fermion pair spectrum.
