  We present a simple description of pion-nucleon ($\pi N$) scattering taking
into account the full complexity of pion absorption and creation on the
nucleon. To do this we solve Dyson-Schwinger equations within the framework of
Time-Ordered Perturbation Theory. This enables us to construct partial wave
separable $ \pi N$ t matrices that can be useful in models of nuclear processes
involving fully dressed nucleons. At the same time, our approach demonstrates
features of Quantum Field Theory, like particle dressing, renormalisation, and
the use of Dyson-Schwinger equations, in a non-relativistic context that is
maximally close to that of Quantum Mechanics. For this reason, this article may
also be of pedagogical interest.
