Semirelativistic Potential Modelling of Bound States: Advocating Due Rigour

TL;DR

This paper discusses simplifying the complex Poincaré-covariant Bethe-Salpeter equation for bound states and emphasizes the importance of rigorous constraints to ensure the reliability of approximate solutions.

Contribution

It advocates for a semirelativistic potential approach that incorporates rigorous spectral constraints to improve the modeling of bound states.

Findings

Highlights the importance of spectral constraints in bound-state modeling

Proposes a semirelativistic potential framework

Emphasizes the need for rigorous validation of approximate solutions

Abstract

The Poincar\'e-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various simplifications. The resulting approximate outcome's reliability can be assessed by applying several rigorous constraints on the nature of the bound-state spectra; most prominent here are existence, number and location of discrete eigenvalues.