  The pion-nucleon scattering is investigated by using several
three-dimensional reduction schemes of the Bethe-Salpeter equation for a model
Lagrangian involving $\pi$, $N$, $\Delta$, $\rho$, and $\sigma$ fields. It is
found that all of the resulting meson-exchange models can give similar good
descriptions of the $\pi N$ scattering data up to 400 MeV. However they have
significant differences in describing the $\pi NN$ and $\pi N\Delta$ form
factors and the $\pi N$ off-shell t-matrix elements. We point out that these
differences can be best distinguished by investigating the near threshold pion
production from nucleon-nucleon collisions and pion photoproduction on the
nucleon. The consequences of using these models to investigate various
pion-nucleus reactions are also discussed.
