Equation for the Nakanishi weight function using the inverse Stieltjes transform.
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= Vg, where V is a two-dimensional integral operator. The prescription for obtaining the kernel V starting with the kernel K of the Bethe-Salpeter equation is given.
Publisher URL: http://arxiv.org/abs/1802.05515
DOI: arXiv:1802.05515v1
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