Link-based causal set propagators in $1+1$ dimensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918470647545856 |
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| author | Hinrichsen, Haye Kastrati, Arsim |
| author_facet | Hinrichsen, Haye Kastrati, Arsim |
| contents | We investigate whether retarded scalar propagators on causal sets can be expressed in terms of the link matrix $\mathbf{L}$. For Poisson sprinklings into $1+1$ dimensional Minkowski spacetime, we show by asymptotic analysis and supporting numerical simulations that the averaged massless retarded propagator is naturally associated with a normalized exponential exp$(\mathbf{L})$. We then extend the construction to the massive case via the usual mass-scattering series and obtain good agreement with the continuum propagator after averaging. Finally, we discuss the inverse kernel exp$(-\mathbf{L})$ as a possible candidate for a discrete d'Alembertian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Link-based causal set propagators in $1+1$ dimensions Hinrichsen, Haye Kastrati, Arsim General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate whether retarded scalar propagators on causal sets can be expressed in terms of the link matrix $\mathbf{L}$. For Poisson sprinklings into $1+1$ dimensional Minkowski spacetime, we show by asymptotic analysis and supporting numerical simulations that the averaged massless retarded propagator is naturally associated with a normalized exponential exp$(\mathbf{L})$. We then extend the construction to the massive case via the usual mass-scattering series and obtain good agreement with the continuum propagator after averaging. Finally, we discuss the inverse kernel exp$(-\mathbf{L})$ as a possible candidate for a discrete d'Alembertian. |
| title | Link-based causal set propagators in $1+1$ dimensions |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.24812 |