Tests of unitary symmetry in strong interactions

After hearing the material presented in the previous talks, one can question the further need for tests of unitary symmetry in strong interactions since it is now clear that unitary symmetry is good enough to play an essential role in any description of strong interactions. However, it is also clear that unitary symmetry is still bad enough to be interesting—in contrast to isospin, which is so good that it cannot teach us anything more about strong interactions. We know that any dynamical theory describing strong interactions must be invariant under isospin transformations. There is nothing further that can be learned about strong interactions from isospin. On the other hand, we know that a dynamical theory correctly describing strong interactions should be invariant under SU 3 transformations only to some approximation. The remarkable regularities observed in the breaking of unitary symmetry (e.g. the mass formula) tell us more about strong interactions than their transformation properties under a particular group. Although these regularities apparently result only from the assumption of certain transformation properties for the symmetry breaking part of the strong interaction, an additional dynamical assumption is required, namely that the symmetry breaking can be treated by first order perturbation theory. It is a test of the detailed dynamics of the system, not merely of the symmetry, to show how such large symmetry breaking effects can be described by what is apparently only first order perturbation theory.