  This is a sort of tutorial where we present many of the tedious details
involved in deriving the correspondence between the number conserving product
of two fermi/bose fields with spin and the corresponding sea/condensate
displacements also with spin. This time we include finite temperature effects
differently by coupling the sea-bosons to an inhomogeneous chemical potential.
It is shown that many of the salient features of the free theory are reproduced
properly by this approach. An attempt is made to be as detailed as possible,
this includes providing formulas for the sea-bosons as well as computing the
finite temperature Fermi correlators.
