A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913654700507136 |
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| author | Dekhil, Roukaya Laudonio, Matteo Oriti, Daniele |
| author_facet | Dekhil, Roukaya Laudonio, Matteo Oriti, Daniele |
| contents | We present the construction of a new state sum model for $4d$ Lorentzian quantum gravity based on the description of quantum simplicial geometry in terms of edge vectors. Quantum states and amplitudes for simplicial geometry are built from irreducible representations of the translation group, then related to the representations of the Lorentz group via expansors, leading to interesting (and intricate) non-commutative structures. We also show how the new model connects to the Lorentzian Barrett-Crane spin foam model, formulated in terms of quantized triangle bivectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors Dekhil, Roukaya Laudonio, Matteo Oriti, Daniele General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We present the construction of a new state sum model for $4d$ Lorentzian quantum gravity based on the description of quantum simplicial geometry in terms of edge vectors. Quantum states and amplitudes for simplicial geometry are built from irreducible representations of the translation group, then related to the representations of the Lorentz group via expansors, leading to interesting (and intricate) non-commutative structures. We also show how the new model connects to the Lorentzian Barrett-Crane spin foam model, formulated in terms of quantized triangle bivectors. |
| title | A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2501.10115 |