Self-Consistent Dispersion-Theoretic Electron-Positron Scattering Amplitude
- 15 April 1971
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 3 (8), 1935-1945
- 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.
Keywords
This publication has 10 references indexed in Scilit:
- Asymptotic Behavior of Scattering Amplitudes in the Relativistic Eikonal ApproximationPhysical Review D, 1970
- Relativistic Balmer Formula Including Recoil EffectsPhysical Review D, 1970
- Theory of the Relativistic H Atom and PositroniumPhysical Review B, 1969
- Exact Determination of the Coulomb Amplitude byS-Matrix MethodsPhysical Review B, 1969
- Regge Poles and anS-Matrix Theory of the Lamb ShiftPhysical Review B, 1969
- Regge Poles in the Scattering of Particles of Unequal Mass. Remark on a Paper of Freedman and WangPhysical Review B, 1967
- Anomalous Magnetic Moment of the Electron, Muon, and NucleonPhysical Review B, 1965
- -Matrix Method for Calculation of Electromagnetic Corrections to Strong InteractionsPhysical Review B, 1964
- Theory of Low-Energy Nucleon-Nucleon ScatteringPhysical Review B, 1960
- Effect of Nuclear Motion on the Fine Structure of HydrogenPhysical Review B, 1948