Time-slicing quantum spacetimes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910183596228608 |
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| author | Majid, Shahn |
| author_facet | Majid, Shahn |
| contents | For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value $t$ of a coordinate time, with corresponding metric in ADM form. We provide a general construction for the spacetime quantum Levi-Civita connection when each spatial slice is replaced by a quantum Riemannian geometry. This is then fully solved for a class of spatial algebras including fuzzy spheres and for any time-dependent spatial quantum metric, shift 1-form and lapse function. The result takes a particularly simple form if the spatial metric evolves in time according to a first order ODE which, in the case of a fuzzy sphere, requires the spatial metric to rotate in time according to the value at each $t$ of the shift vector. As an application, our results provide in principle fuzzy versions of most (pseudo)-Riemannian manifolds. We also fully solve the case of rotationally invariant spacetimes with angular directions replaced by a discrete circle, including a new $\Bbb Z_n$-FLRW model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Time-slicing quantum spacetimes Majid, Shahn General Relativity and Quantum Cosmology Quantum Algebra For quantum field theory on curved spacetimes, a critical role is played by their foliation into spacelike time-slices at each value $t$ of a coordinate time, with corresponding metric in ADM form. We provide a general construction for the spacetime quantum Levi-Civita connection when each spatial slice is replaced by a quantum Riemannian geometry. This is then fully solved for a class of spatial algebras including fuzzy spheres and for any time-dependent spatial quantum metric, shift 1-form and lapse function. The result takes a particularly simple form if the spatial metric evolves in time according to a first order ODE which, in the case of a fuzzy sphere, requires the spatial metric to rotate in time according to the value at each $t$ of the shift vector. As an application, our results provide in principle fuzzy versions of most (pseudo)-Riemannian manifolds. We also fully solve the case of rotationally invariant spacetimes with angular directions replaced by a discrete circle, including a new $\Bbb Z_n$-FLRW model. |
| title | Time-slicing quantum spacetimes |
| topic | General Relativity and Quantum Cosmology Quantum Algebra |
| url | https://arxiv.org/abs/2605.00520 |