Schroedinger models for solutions of the Bethe-Salpeter equation in Minkowski space

TL;DR

This paper introduces a method to derive nonrelativistic potential models from the Minkowski-space Bethe-Salpeter equation, simplifying the analysis of bound states of two particles by capturing their key features without complex relativistic calculations.

Contribution

The authors develop a geometric spectral inversion technique that constructs Schrödinger models from spectral data of the Bethe-Salpeter equation, accommodating singular potentials.

Findings

Successfully models bound state features like masses and form factors

Provides a simpler alternative to the Bethe-Salpeter formalism

Extends spectral inversion to singular interaction potentials

Abstract

By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space formulation of the homogeneous Bethe-Salpeter equation describing bound states of two spinless particles a Schroedinger approach to such states in terms of nonrelativistic potential models. This spectrally equivalent modeling of bound states yields their qualitative features (masses, form factors, etc.) without having to deal with the more involved Bethe-Salpeter formalism.