Analytic Quest for Confining Interaction Kernels in Instantaneous Bethe-Salpeter Equations

TL;DR

This paper analyzes the Salpeter equation in hadron physics to identify interaction kernels that produce stable bound states, ensuring physical consistency in modeling confinement within quantum field theories.

Contribution

It provides a systematic spectral analysis method to select confining interaction kernels that yield stable bound states in the Salpeter equation.

Findings

Identifies conditions for stable bound states in the Salpeter equation.

Distinguishes kernels leading to real, bounded spectra.

Offers a framework for consistent confinement modeling.

Abstract

The Salpeter equation, a standard tool in hadron physics, constitutes a well-defined three-dimensional approximation to the Bethe-Salpeter formalism for the description of bound states within quantum field theories. However, if confinement is implemented in a too careless manner, the Salpeter equation might predict unstable states where only truly bound states are expected. A systematic spectral analysis of the Salpeter equation might serve to single out those Bethe-Salpeter interaction kernels which indeed yield stable bound states, with associated energy eigenvalues belonging to a real discrete spectrum bounded from below.