Instantaneous Bethe-Salpeter Equation with Exact Propagators

TL;DR

This paper derives an instantaneous Bethe-Salpeter equation incorporating exact propagators, generalizing the Salpeter equation by removing the assumption of free propagation, thus providing a more accurate bound-state description.

Contribution

It introduces an instantaneous Bethe-Salpeter equation with full propagators, extending the Salpeter equation without assuming free propagation of constituents.

Findings

Derivation of the instantaneous Bethe-Salpeter equation with exact propagators

Generalization of the Salpeter equation

Provides a more accurate bound-state formalism

Abstract

Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe-Salpeter formalism for the description of bound states, an instantaneous form of the Bethe-Salpeter equation with exact (i.e., full) propagators of the bound-state constituents. This instantaneous equation generalizes the well-known Salpeter equation the derivation of which needs the additional assumption of free propagation of the bound-state constituents.