  We construct a class of microscopic electron models with exact SO(5) symmetry
between antiferromagnetic and d-wave superconducting ground states. There is an
exact one-to-one correspondence between both single-particle and collective
excitations in both phases. SO(5) symmetry breaking terms can be introduced and
classified according to irreducible representations of the exact SO(5) algebra.
The resulting phase diagram and collective modes are identical to that of the
SO(5) nonlinear sigma model.
