Current algebra, infinite momentum and sum rules

Abstract

We summarize results obtained so far by using an approximation called SU(3) approximation and a chiral SU(3) ⊗ SU(3) charge-charge or charge-charge density algebra. The approximation concerns the vector charge operator V K which is an SU(3) raising and lowering operator in the symmetry limit. We assume that even in broken symmetry the operator V K still acts as a generator, to a good approximation, in an appropriately chosen infinite momentum limit. We derive many broken SU(3) coupling constant sum rules as well as the first SU(3) and the first chiral SU(2) ⊗ SU(2) spectral function sum rules. However, we are never led to the problematic second spectral function sum rules. The inclusion of the time derivative of the operator V K in this approach allows us to derive not only the SU(3) mass formulae but also the SU(6)-like intermultiplet mass formulae and the sum rules involving the masses and physical coupling constants that agree rather well with experiment.