  We set up the effective field theories which describe the SO(5)-invariant
picture of the high-Tc cuprates in various regimes. We use these to get
quantitative conclusions concerning the size of SO(5)-breaking effects. We
consider two applications in detail: (i) the thermodynamic free energy, which
describe the phase diagram and critical behaviour, and (ii) the Lagrangian
governing the interactions of the pseudo-Goldstone bosons with each other and
with the electron quasiparticles deep within the ordered phases. We use these
effective theories to obtain predictions for the critical behaviour near the
possible bicritical point and the pseudo-Goldstone boson dispersion relations,
as well as some preliminary results concerning their contribution to response
functions. We systematically identify which predictions are independent of the
microscopic details of the underlying electron dynamics, and which depend on
more model-dependent assumptions.
