  The linear sigma model with pions and sigma coupled to baryons and a
(massive) gauge vector meson is considered for the description of a finite
baryonic density system. The stability equation for the bound system is studied
in the homogeneous limit considering quantum fluctuations for the scalar and
pseudo scalar fields within a variational method with truncations. Nearly exact
solutions for the stability equation which also solve the field equations are
sought semi-analytically. Bosonic fields are found to have non zero expected
classical values at finite density corresponding to condensates of dynamical
symmetry breakings. The two components of baryon field, neutron and proton for
example, acquire different masses due to the isospin symmetry breaking and
these states may even oscillate in the medium. There is a non trivial solution
for the (massive) vector meson field indicating the occurrence of a gauge
dynamical symmetry breaking at finite density typical of a superconductor.
