Algebraic approach to quantum gravity IV: applications
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914454185181184 |
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| author | Majid, Shahn |
| author_facet | Majid, Shahn |
| contents | We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature fluctuations in a single-plaquette model of quantum gravity, derivation of the Kaluza-Klein ansatz as a consequence of quantum spacetime, exactly conserved Noether charges from variational calculus on a lattice, and a new theory of classical and quantum geodesics. The latter leads to a theory of generally covariant quantum mechanics applicable in General Relativity with intriguing first results for the case of a black-hole. We discuss several open problems past and present, and how they might be addressed going forward. New results include a phase transition for Euclidean quantum gravity on a 4-pointed star. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06118 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebraic approach to quantum gravity IV: applications Majid, Shahn General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Algebra We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature fluctuations in a single-plaquette model of quantum gravity, derivation of the Kaluza-Klein ansatz as a consequence of quantum spacetime, exactly conserved Noether charges from variational calculus on a lattice, and a new theory of classical and quantum geodesics. The latter leads to a theory of generally covariant quantum mechanics applicable in General Relativity with intriguing first results for the case of a black-hole. We discuss several open problems past and present, and how they might be addressed going forward. New results include a phase transition for Euclidean quantum gravity on a 4-pointed star. |
| title | Algebraic approach to quantum gravity IV: applications |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2604.06118 |