Few-Body Systems

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Equation for the Nakanishi Weight Function Using the Inverse Stieltjes Transform

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  1. Light Cone 2017

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.

Notes

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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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lebedev Physical InstituteMoscowRussia
  2. 2.Institut de Physique Nucleaire, IN2P3-CNRSUniversité Paris-SudOrsay CedexFrance
  3. 3.Instituto Tecnológico de AeronáuticaDCTAS. José dos CamposBrazil

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