Minimal covariant quantum space-time
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910814172086272 |
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| author | Manta, Alessandro Steinacker, Harold C. |
| author_facet | Manta, Alessandro Steinacker, Harold C. |
| contents | We discuss minimal covariant quantum space-time ${\cal M}^{1,3}_0$, which is defined through the minimal doubleton representation of $\mathfrak{so}(4,2)$. An elementary definition in terms of generators and relations is given. This space is shown to admit a semi-classical interpretation as quantized twistor space ${\mathbb C} P^{1,2}$, viewed as a quantized $S^2$-bundle over a 3+1-dimensional $k=-1$ FLRW space-time. In particular we find an over-complete set of (quasi-) coherent states, with a large hierarchy between the uncertainty scale and the geometric curvature scale. This provides an interesting background for the IKKT model, leading to a $\mathfrak{hs}$-extended gravitational gauge theory, which is free of ghosts due to the constraints on phase space arising from the doubleton representation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_02498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal covariant quantum space-time Manta, Alessandro Steinacker, Harold C. High Energy Physics - Theory General Relativity and Quantum Cosmology We discuss minimal covariant quantum space-time ${\cal M}^{1,3}_0$, which is defined through the minimal doubleton representation of $\mathfrak{so}(4,2)$. An elementary definition in terms of generators and relations is given. This space is shown to admit a semi-classical interpretation as quantized twistor space ${\mathbb C} P^{1,2}$, viewed as a quantized $S^2$-bundle over a 3+1-dimensional $k=-1$ FLRW space-time. In particular we find an over-complete set of (quasi-) coherent states, with a large hierarchy between the uncertainty scale and the geometric curvature scale. This provides an interesting background for the IKKT model, leading to a $\mathfrak{hs}$-extended gravitational gauge theory, which is free of ghosts due to the constraints on phase space arising from the doubleton representation. |
| title | Minimal covariant quantum space-time |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2502.02498 |