Theory of the Off-Shell Pion-NucleontMatrix

A theory of the off-shell $\pi N$ $t$ matrix is proposed. The theory, which employs dispersion-theoretic techniques, incorporates the on-shell information, including the inelasticities, and derives the additional information required to continue off shell from the underlying field theory. Results are presented for the $P$-wave states and are compared with those of other approaches.