Equation for the Nakanishi weight function using the inverse Stieltjes transform
arXiv:1802.05515 · doi:10.1007/s00601-018-1339-1
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= 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.
7 pages
References in corpus (10)
- The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
- Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
- Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
- Solving Bethe-Salpeter scattering state equation in Minkowski space
- Bethe-Salpeter bound-state structure in Minkowski space
- Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
- Bound state equation for the Nakanishi weight function
- Bound state structure and electromagnetic form factor beyond the ladder approximation
- Euclidean to Minkowski Bethe-Salpeter amplitude and observables
- Integral transform methods: a critical review of various kernels