Invariant Amplitudes for Photon Processes

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Abstract
A method for constructing independent invariant amplitudes for photon processes which satisfy gauge invariance and are free from both kinematic singularities and zeros (constraints) is proposed. The method is based on the use of a simple projection operator which automatically ensures gauge invariance at every stage. The invariant amplitudes for pion photoproduction, pion Compton scattering, and nucleon Compton scattering are found. Previously known results in the first two cases are reproduced and their interpretation is clarified. For nucleon Compton scattering the result is new. Comparisons are made between these invariant amplitudes, the Hearn and Leader amplitudes, and the regularized helicity amplitudes. The Mandelstam representation may be applied to these kinematic-singularity-free and zero-free amplitudes without any ad hoc substractions. All known low-energy theorems on photon processes can be derived most directly from these invariant amplitudes.