Equations for on-shell partial-wave amplitudes in the boundary condition model

In the framework of a potential model a representation is established for the on-shell partial-wave scattering amplitude, this representation making it possible to formulate a system of equations for calculating the phase shifts and, using the fairly general requirements of $S$-matrix theory, generalize the method to the relativistic case. The representation can be applied to the problem of taking into account meson and quarkgluon degrees of freedom in hadron-hadron scattering. The connection between the method and the Jaffe–Low $P$-matrix formalism is established, and this makes it possible to relate the parameters that arise in the solution of the dispersion relations for the partial-wave amplitudes to quantities that can be calculated in the quark bag model. The proposed approach can also be regarded as an alternative to the Feshbach–Lomon boundary condition method.