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 πN and γπN 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 πN → πN and γN → πN .Typeset using REVT E X

A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the πN and γπN thresholds. The final amplitude can be written in terms of a distorted wave in the final πN channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.Most calculations to date for pion photoproduction on a single nucleon have included two ingredients: (i) A Born term which is taken to be gauge invariant. (ii) A final state interaction or distortion that is needed to satisfy the Watson theorem or unitarity.However, the inclusion of the pionic degrees of freedom into the problem changes the current and charge distribution and thus the coupling of the photon to the nucleon.Hence any consistent theory of pion photoproduction has to include the effect of the pionic degrees of freedom on the charge and current distribution. In other words one needs to satisfy unitarity and gauge invariance at the same time. Clearly, the inclusion of both of these symmetries to all orders requires a full solution to the field theory. Here, we