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Riemann surfaces and partial wave models

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Abstract

Within the context of simple partial wave models for elastic scattering the problem of uniformizing the partial wave amplitude and classifying its Riemann surface is studied. Starting with the analytic continuation of the amplitude an analysis of the Riemann surface is made through its group of covering transformations relative to a simpler base surface. A model based on the Yukawa potential is studied in this manner and the Riemann surface of interest is found to be the universal covering surface of the thrice punctured sphere. The uniformization of the amplitude can be done explicitly in this case by use of the elliptic modular function. In terms of the uniformizing variable, the original discontinuity relations for the amplitude then reduce to functional equations involving elements of the modular group.

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Authors and Affiliations

  1. Department of Physics, Queen Mary College, University of London, UK

    R. B. Jones

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  1. R. B. Jones
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Jones, R.B. Riemann surfaces and partial wave models. Commun.Math. Phys. 17, 143–155 (1970). https://doi.org/10.1007/BF01646598

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  • DOI: https://doi.org/10.1007/BF01646598

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