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The pion-nucleon scattering is investigated by using severalthree-dimensional reduction schemes of the Bethe-Salpeter equation for a modelLagrangian involving $\pi$, $N$, $\Delta$, $\rho$, and $\sigma$ fields. It isfound that all of the resulting meson-exchange models can give similar gooddescriptions of the $\pi N$ scattering data up to 400 MeV. However they havesignificant differences in describing the $\pi NN$ and $\pi N\Delta$ formfactors and the $\pi N$ off-shell t-matrix elements. We point out that thesedifferences can be best distinguished by investigating the near threshold pionproduction from nucleon-nucleon collisions and pion photoproduction on thenucleon. The consequences of using these models to investigate variouspion-nucleus reactions are also discussed.Comment: 29 pages, 3 Tables, 7 figures, Latex, changed the unit of figures  4,5,6 and

physical review. c. nuclear physics/physical review. c, nuclear physics

Meson-exchange<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>N</mml:mi></mml:math>models in three-dimensional Bethe-Salpeter formulation

Meson-exchangeπNmodels in three-dimensional Bethe-Salpeter formulation