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Equation for the Nakanishi Weight Function Using the Inverse Stieltjes Transform

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Abstract

The bound state Bethe–Salpeter amplitude was expressed by Nakanishi in terms of a smooth weight function g. By using the generalized Stieltjes transform, we derive an integral equation for the Nakanishi function g for a bound state case. It has the standard form \(g= \hat{\mathcal V} g\), where \(\hat{\mathcal V} \) is a two-dimensional integral operator. The prescription for obtaining the kernel \({\mathcal V} \) starting with the kernel K of the Bethe–Salpeter equation is given.

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Acknowledgements

We are indebted to G. Salmé for useful discussions. T.F. thanks CNPq, CAPES and FAPESP of Brazil. V.A.K. thanks the support of FAPESP, the Grant #2015/22701-6 and is sincerely grateful for kind hospitality to Theoretical Nuclear Physics Group in ITA, São José dos Campos, Brazil, where the main part of this research was carried out.

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Authors and Affiliations

  1. Lebedev Physical Institute, Leninsky Prospekt 53, Moscow, Russia, 119991

    V. A. Karmanov

  2. Institut de Physique Nucleaire, IN2P3-CNRS, Université Paris-Sud, 91406, Orsay Cedex, France

    J. Carbonell

  3. Instituto Tecnológico de Aeronáutica, DCTA, S. José dos Campos, 12228-900, Brazil

    T. Frederico

Authors
  1. V. A. Karmanov
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  2. J. Carbonell
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  3. T. Frederico
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Correspondence to V. A. Karmanov.

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Karmanov, V.A., Carbonell, J. & Frederico, T. Equation for the Nakanishi Weight Function Using the Inverse Stieltjes Transform. Few-Body Syst 59, 27 (2018). https://doi.org/10.1007/s00601-018-1339-1

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