Poincaré-invariant coupled-channel models for meson photoproduction

A general procedure for constructing Poincaré-invariant mass operators in a helicity basis is presented. The procedure is developed in the framework of the instant form of relativistic quantum mechanics, but it can be easily extended to other forms. The method is used to extend a previously developed Poincaré-invariant coupled-channel model for the pion-nucleon system to include a photon-nucleon channel. This makes it possible to carry out calculations on photoproduction from nucleons that satisfy exactly the requirements of special relativity. Methods are given for deriving potentials that couple the photon-nucleon channel to the pionnucleon channel. These potentials are invariant under gauge transformations of the photon's polarization vector. Amplitudes obtained by solving the Lippmann-Schwinger equations that arise from the Poincaré-invariant mass operators satisfy unitarity, and hence Watson's theorem for photoproduction amplitudes. The methods presented can also be used to develop models for the photoproduction of η and K mesons, as well as vector mesons.