Current algebra and superconvergence

Abstract

We study the implication of the algebra of currents and the concepts of unitarity, analyticity and high energy behaviour of scattering amplitudes to investigate sum rules for some scattering processes. In Chapter I we introduce the concept of current algebras and show how to derive sum rules starting from equal time commutators. In Chapter II we apply the formulation developed in Chapter I, to the equal time commutator of axial vector charge and the isovector electromagnetic current, and obtain a relation between the πN*N* p-wave coupling constant to s-wave πNN coupling constant. In Chapter III we show how to derive sum rule for strongly interacting particles starting from commutator of weak currents. This leads us to examine whether we could derive the same sum rules without the help of current commutator , and using only the concepts of pure strong interaction, namely unitarity, analyticity, high energy behaviour. We find that this can be done. We then apply the formalism to derive sum rules for πD (N*1525) scattering, obtaining a value for the πDD coupling constant. In Chapter IV, we develop and apply the helicity formalism to obtain superconvergence relation for πN → πN* and πN* →πN*. We obtain a relation between πNN coupling constant g(_1) and p-wave coupling constant g(_3). We also find the value of g(_3) in terms of g(_2), the πNN* coupling constant.