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Self-Consistent Dispersion-Theoretic Electron-Positron Scattering Amplitude
Phys. Rev. D 3, 1935 – Published 15 April, 1971Erratum Phys. Rev. D 4, 603 (1971)
DOI: https://doi.org/10.1103/PhysRevD.3.1935
Abstract
A method is outlined for the construction of dispersion-theoretic electromagnetic scattering amplitudes for processes in which bound states may appear; in particular, the electron-positron system is examined. A Lorentz-covariant spinor amplitude is exhibited which is analytic, cutoff independent, and crossing symmetric, which has the correct double-spectral functions through second order in the fine-structure constant , and which reduces to the usual Born approximation in lowest order. Moreover, the amplitude displays Regge asymptotic behavior and the positronium Regge poles. Self-consistency requires that the positronium poles appear at the correct position and with the proper residue, and that the amplitude possesses a well-defined Jacob-Wick expansion. It is found that this second-order amplitude provides a suitable basis for iterative calculation of the higher-order terms using the same procedure.
Erratum
Self-Consistent Dispersion-Theoretic Electron- Positron Scattering Amplitude
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