Crossing Relations and the Prediction of Symmetries in a Soluble Model

Publisher Website
Google Scholar
Abstract
The two-channel static model, incorporating unitarity and a nontrivial crossing relation, is known to be exactly soluble for a specific choice of the crossing matrix. The solution, obtained by Wilson and independently by Wanders, is largely independent of a number of the dynamical assumptions of the static model and may, therefore, indicate properties of more realistic models for the strong interactions. We have generalized the two-channel problem by introducing arbitrary crossing matrices of a type suitable to the static model. We ask if the requirement that exact solutions exist leads to restrictions upon the crossing matrices and hence to the prediction of symmetries. The answer is in the negative; we exhibit solutions for all values of the parametrized crossing matrix. However, special solutions of a particularly simple form exist only for crossing matrices corresponding to the symmetry group SU(2). The relationship between these special solutions and the general solution is discussed.