  We use generalized coherent states to analyze the SO(5) theory of
high-temperature superconductivity and antiferromagnetism. We demonstrate that
the SO(5) symmetry can be embedded in a larger algebra that allows it to be
interpreted as a critical dynamical symmetry interpolating between
antiferromagnetic and superconducting phases. This dynamical interpretation
suggests that SO(5) defines a phase with the character of a spin-glass for a
significant range of doping.
