Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913238293151744 |
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| author | Jia, Shaoyang |
| author_facet | Jia, Shaoyang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08698 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model Jia, Shaoyang Nuclear Theory High Energy Physics - Theory 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. |
| title | Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model |
| topic | Nuclear Theory High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.08698 |