Subtractions in Dispersion Relations
- 25 January 1967
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 153 (5), 1449-1454
- https://doi.org/10.1103/PhysRev.153.1449
Abstract
Assuming the unitarity bound in the physical region on a partial-wave amplitude for an elastic scattering process, and assuming further that the amplitude satisfies a dispersion relation, it is shown that the necessity for subtractions in order to make the integral over the left-hand cut converge implies an oscillatory behavior of the discontinuity across the left-hand cut, the violence of the oscillations increasing with increasing number of subtractions. A theorem given by Sugawara and Kanazawa is provided with a rigorous proof and is applied to pion-nucleon and kaon-nucleon dispersion relations.Keywords
This publication has 9 references indexed in Scilit:
- New Determination of the Pion-Nucleon Coupling Constant and-Wave Scattering LengthsPhysical Review Letters, 1965
- Connection Between the Asymptotic Behavior and the Sign of the Discontinuity in One-Dimensional Dispersion RelationsPhysical Review B, 1964
- Determination of Pion-Nucleon Parameters and Phase Shifts by Dispersion RelationsReviews of Modern Physics, 1963
- s-wave pion-nucleon scattering and pion-pion interactionsAnnals of Physics, 1962
- Subtractions in Dispersion RelationsPhysical Review B, 1961
- Construction of the Perturbation Series for Transition Amplitudes from their Analyticity and Unitarity PropertiesPhysical Review B, 1959
- Analytic Properties of Transition Amplitudes in Perturbation TheoryPhysical Review B, 1959
- Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General TheoryPhysical Review B, 1958
- Notes on the Theory of Series (XI): On Tauberian TheoremsProceedings of the London Mathematical Society, 1930