A gauge invariant unitary theory for pion photoproduction
  The Ward-Takahashi identities are central to the gauge invariance of the photoproduction amplitude. Here we demonstrate that unitarity and in particular the inclusion of both the $\pi N$ and $\gamma\pi N$ thresholds on equal footing yields a photoproduction amplitude that satisfies both two-body unitarity and the generalized Ward-Takahashi identities. The final amplitude is a solution of a set of coupled channel integral equations for the reactions $\pi N\rightarrow\pi N$ and $\gamma N\rightarrow\pi N$. % Figures available from the authors upon request, % e-mail: phchv@pippin.cc.flinders.edu.au % Submitted to Physical Review C 
C. H. M. van Antwerpen and I. R. Afnan