  A path integration formulation for the finite density and temperature
problems is shown to be consistent with the thermodynamics using an 8 component
``real'' representation for the fermion fields by applying it to a free fermion
system. A relativistic quantum field theory is shown to be smoothly approached
at zero temperature by a real-time thermal field theory so derived even at a
finite density. The analysis leads to a new representation for the fermion
fields which is shown to be inequivalent to the conventional 4 component theory
at the quantum level by having a mirror universe with observable effects and to
be better behaved at short distances.
