Microscopic Electron Models with Exact SO(5) Symmetry

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.