Vertex functions in the dispersion theory of current algebras

Abstract

Vertex functions are investigated in the dispersion theory of current algebras. The cases considered constitute a particularly simple opportunity to study the mutual consistency of the various assumptions usually used. It is demonstrated that the assumption of unsubtracted dispersion relations for integrals over matrix elements of current commutators leads to contradictions, when applied to all invariants in the kinematic decomposition of the tensors. These difficulties can be avoided only if one accepts operators of isospin one in Schwinger terms. The same contradictions are found, if in the infinitemomentum approach one admits commutators of current time and space components. The equivalence of the two approaches depends on the validity of superconvergence relations for the asymptotic behaviour of some form factors.