Dispersion Relations for Compton Scattering

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Abstract
The perturbation formulas for Compton scattering with radiative corrections are written as dispersion relations. The purpose is to learn something about (1) the number of subtractions that are needed in the relations, (2) the analytic continuation of the scattering amplitude into the unphysical region, and (3) the role of the infrared divergence. It is found that one subtraction is needed to obtain dispersion relations but that these equations still depend on the fictitious mass of the photon. To obtain relations which contain only physical quantities another subtraction is made. It is suggested that the imaginary part of the amplitude has fewer singularities than the amplitude itself, and consequently may, in some cases, be continued by means of the phase-shift expansion. Finally, it is shown that the Born approximation is equivalent to the so-called one-electron-intermediate-state contribution to the dispersion relation.

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