Convergent perturbation expressions and analyticity properties in static field-theoretic models

Simplified field-theoretic models, consisting of a charged-pion field coupled linearly and quadratically to a fixed extended nucleon with spin and isospin, are considered. For small couplings it is shown that perturbation theory converges and yields the dressed one-nucleon states and the resolvent of the total Hamiltonian for complex energy. The elastic-scattering and one-pion production amplitudes are shown i) to be analytic functions of the respective complex energies and ii) to be given by convergent perturbation expansions in certain regions of the associated complex energy planes. (14 refs).