bound state equation for the nakanishi weight function

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ID: 215533
2017
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Abstract
The bound state Bethe–Salpeter amplitude was expressed by Nakanishi using a two-dimensional integral representation, in terms of a smooth weight function g, which carries the detailed dynamical information. A similar, but one-dimensional, integral representation can be obtained for the Light-Front wave function in terms of the same weight function g. By using the generalized Stieltjes transform, we first obtain g in terms of the Light-Front wave function in the complex plane of its arguments. Next, a new integral equation for the Nakanishi weight function g is derived for a bound state case. It has the standard form g=Ng, where N is a two-dimensional integral operator. We give the prescription for obtaining the kernel N starting with the kernel K of the Bethe–Salpeter equation. The derivation is valid for any kernel given by an irreducible Feynman amplitude.
Reference Key
carbonell2017physicsbound Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;J. Carbonell;T. Frederico;V.A. Karmanov
Journal ACS chemical biology
Year 2017
DOI
10.1016/j.physletb.2017.04.016
URL
http://www.sciencedirect.com/science/article/pii/S0370269317302903
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