Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model
Abstract
In order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude (BSA) and the Bethe-Salpeter wave function (BSWF). We then derive the explicit integral equations for the corresponding spectral functions from the BSE for states of scalar particles bound by a scalar-particle exchange interaction, where the propagators of constituents are allowed to be fully dressed. These integral equations are subsequently solved numerically in the variation of the Wick-Cutkosky model with massive exchange particles, where an algorithm of adaptive mash grid is proposed. The equations and algorithm we develop here serve as the foundation of Minkowski-space formulation of BSE for bound states of fermions.
Keywords
Cite
@article{arxiv.2312.08698,
title = {Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model},
author = {Shaoyang Jia},
journal= {arXiv preprint arXiv:2312.08698},
year = {2024}
}