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arXiv · 2312.08698

Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model

Shaoyang Jia
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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 $2$ 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.

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Shaoyang Jia. 2023-12-14. Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model. https://doi.org/10.1103/physrevd.109.036020

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