Bethe-Salpeter equation with cross-ladder kernel in Minkowski and Euclidean spaces

TL;DR

This paper introduces a new method for solving the Bethe-Salpeter equation applicable to any kernel from irreducible Feynman graphs, providing solutions in Minkowski and Euclidean spaces, and calculating binding energies and form factors.

Contribution

The paper presents a novel method for solving the Bethe-Salpeter equation with complex kernels, extending solutions to both Minkowski and Euclidean spaces.

Findings

Successfully computed Bethe-Salpeter amplitudes in Minkowski and Euclidean spaces.

Determined binding energies for ladder plus cross-ladder kernels.

Calculated electromagnetic form factors for the bound states.

Abstract

Some results obtained by a new method for solving the Bethe-Salpeter equation are presented. The method is valid for any kernel given by irreducible Feynman graphs. The Bethe-Salpeter amplitude, both in Minkowski and in Euclidean spaces, and the binding energy for ladder + cross-ladder kernel are found. We calculate also the corresponding electromagnetic form factor.