A new 2+1 coherent spin-foam vertex for quantum gravity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914932996440064 |
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| author | Simão, José Diogo |
| author_facet | Simão, José Diogo |
| contents | We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions, allowing for both space- and time-like boundaries. The model is based on two main requirements: that it should be structurally similar to its well-known Euclidean analog, and that geometricity should be recovered in the semiclassical regime. To this end we introduce new coherent states for space-like boundary edges, derived from the continuous series of unitary $\mathrm{SU}(1,1)$ representations. We show that the relevant objects in the amplitude can be written in terms of the defining representation of the group, just as so happens in the Euclidean case. We derive an expression for the semiclassical amplitude at large spins, showing it relates to the Lorentzian Regge action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new 2+1 coherent spin-foam vertex for quantum gravity Simão, José Diogo General Relativity and Quantum Cosmology High Energy Physics - Theory We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions, allowing for both space- and time-like boundaries. The model is based on two main requirements: that it should be structurally similar to its well-known Euclidean analog, and that geometricity should be recovered in the semiclassical regime. To this end we introduce new coherent states for space-like boundary edges, derived from the continuous series of unitary $\mathrm{SU}(1,1)$ representations. We show that the relevant objects in the amplitude can be written in terms of the defining representation of the group, just as so happens in the Euclidean case. We derive an expression for the semiclassical amplitude at large spins, showing it relates to the Lorentzian Regge action. |
| title | A new 2+1 coherent spin-foam vertex for quantum gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.05993 |