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Description
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 [1]. It has the standard form g= Ng, where N is a two-dimensional integral operator, in contrast to previously used equation which contained the integrals in its both parts. 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.
[1] J. Carbonell, T. Frederico, V.A. Karmanov, Phys. Lett. B, 769, 418 (2017).
