A crossing symmetric $\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\pi NN$ vertex of the same potential model.Comment: 6 pages, 2 figures; contribution to the proceedings of "Achievements and New Directions in Subatomic Physics: Workshop in Honour of Tony Thomas's 60th Birthday", Special Centre for the Subatomic Structure of Matter, Adelaide, South Australia, February 15 - February 19, 2010

Pion photoproduction amplitudes are calculated from a set of equations that have been derived by coupling an external photon to all places in a dressed pion-nucleon vertex. The calculation is consistent with gauge invariance, charge conservation, unitarity and covariance. To provide input to the photoproduction amplitude, a photon-nucleon vertex is calculated from a set of equations derived by complete attachment of photons to a dressed nucleon propagator. We check the accuracy of this vertex by extracting its nucleon electromagnetic form factors.

No abstract