Solution of the Bethe-Salpeter equation in Minkowski space for a two fermion system

TL;DR

This paper extends a Minkowski space solution method for the Bethe-Salpeter equation to two-fermion systems, providing numerical solutions and amplitudes that agree with Euclidean results.

Contribution

It introduces a novel approach to solve the Bethe-Salpeter equation for fermions in Minkowski space using Nakanishi representation and light-front projection.

Findings

Numerical solutions for J=0 bound states are obtained.

Binding energies closely match Euclidean space results.

Minkowski space amplitudes are successfully computed.

Abstract

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.