Solutions of the Bethe-Salpeter equation in Minkowski space and applications to electromagnetic form factors

TL;DR

This paper introduces a novel method for solving the Bethe-Salpeter equation directly in Minkowski space using Nakanishi representation and light-front projection, enabling calculation of electromagnetic form factors for spinless and fermionic systems.

Contribution

The paper develops a new approach to solve the Bethe-Salpeter equation in Minkowski space applicable to various kernels and particle spins, improving direct Minkowski-space calculations.

Findings

Successfully computed Minkowski-space Bethe-Salpeter amplitudes.

Obtained electromagnetic form factors and validated against Euclidean results.

Demonstrated method's applicability to spinless and fermionic systems.

Abstract

We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the light-front plane. The method is valid for any kernel given by the irreducible Feynman graphs and for systems of spinless particles or fermions. The Bethe-Salpeter amplitudes in Minkowski space are obtained. The electromagnetic form factors are computed and compared to the Euclidean results.