  We construct a microscopic model of electron interactions which gives rise to
both superconductivity and antiferromagnetism, and which admits an approximate
SO(5) symmetry that relates these two phases. The symmetry can be exact, or it
may exist only in the long-wavelength limit, depending on the detailed form of
the interactions. We compute the macroscopic Landau-Ginzburg free energy for
this model as a function of temperature and doping, by explicitly integrating
out the fermions. We find that the resulting phase diagram can resemble that
observed for the cuprates, with the antiferromagnetism realized as a spin
density wave, whose wavelength might be incommensurate with the lattice spacing
away from half filling.
