# Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

## TL;DR

This paper presents a direct Minkowski space solution to the scalar three-body Bethe-Salpeter equation with zero-range interaction, accurately handling singularities and comparing results with Euclidean space calculations.

## Contribution

It introduces a novel direct Minkowski space approach for solving the three-body Bethe-Salpeter equation without assumptions, handling singularities effectively.

## Key findings

- Binding energies agree with Euclidean space results
- Transverse amplitudes match Euclidean calculations
- Method effectively manages propagator singularities

## Abstract

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.