  The question of the allowed signs for the static dielectric function for
exactly homogeneous ground states in many body systems is further analyzed. The
discussion is restricted to zero temperature situation. Firstly, it is argued
that the positivity is equivalent to the requirement that the work needed for
to adiabatically connect a static charge density, be positive. In particular
the rule seems to be a fully appropriate stability condition if the system
interacts with a freely moving but coulomb interacting jellium. This situation
is common in thermodynamical equilibrium discussions, in which the system can
be stable or not in dependence of the relaxation of some external constraints.
Further, an argument based in a quantized electromagnetic field treatment is
also given. It requires the positivity of the dielectric function as an
intrinsic stability condition for the charged system independently of the
jellium dynamics.Possible inmplications for the more complex finite temperature
situation are commented.
