  S.C. Zhang has put forward the idea that high-temperature-superconductors can
be described in the framework of an SO(5)-symmetric theory in which the three
components of the antiferromagnetic order-parameter and the two components of
the two-particle condensate form a five-component order-parameter with SO(5)
symmetry. Interactions small in comparison to this strong interaction introduce
anisotropies into the SO(5)-space and determine whether it is favorable for the
system to be superconducting or antiferromagnetic. Here the view is expressed
that Zhang's derivation of the effective interaction V_{eff} based on his
Hamiltonian H_a is not correct. However, the orthogonality constraints
introduced several pages after this 'derivation' give the key to an effective
interaction very similar to that given by Zhang. It is shown that the
orthogonality constraints are not rigorous constraints, but they maximize the
entropy at finite temperature. If the interaction drives the ground-state to
the largest possible eigenvalues of the operators under consideration
(antiferromagnetic ordering, superconducting condensate, etc.), then the
orthogonality constraints are obeyed by the ground-state, too.
