Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions

TL;DR

This paper derives exact analytical solutions to the instantaneous Bethe-Salpeter equation under simplifying assumptions, enhancing understanding of relativistic bound states in quantum field theory.

Contribution

It provides the first explicit solutions to the Bethe-Salpeter equation with instantaneous interactions, linking solutions directly to the interaction potentials.

Findings

Exact solutions for specific interaction models

Analytical expressions relating solutions to interaction kernels

Improved understanding of relativistic bound state formation

Abstract

The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.