FLRW embeddings in $\mathbb{R}^{n+2}$, differential geometry and conformal photon propagator
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| Format: | Preprint |
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2025
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| _version_ | 1866915887831842816 |
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| author | Huguet, E. Queva, J. Renaud, J. |
| author_facet | Huguet, E. Queva, J. Renaud, J. |
| contents | This paper introduces differential-geometric methods to study $n$-dimensional locally conformally flat spaces as submanifolds in $\mathbb{R}^{n+2}$. We derive explicit formulas relating intrinsic and ambient differential-geometric objects, including curvature tensors, the codifferential and laplacian operators. We apply this approach to Friedmann-Lemaître-Robertson-Walker (FLRW) spaces using newfound embedding formulas, obtaining new and simplified expressions for the photon propagator in four dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10901 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | FLRW embeddings in $\mathbb{R}^{n+2}$, differential geometry and conformal photon propagator Huguet, E. Queva, J. Renaud, J. Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry This paper introduces differential-geometric methods to study $n$-dimensional locally conformally flat spaces as submanifolds in $\mathbb{R}^{n+2}$. We derive explicit formulas relating intrinsic and ambient differential-geometric objects, including curvature tensors, the codifferential and laplacian operators. We apply this approach to Friedmann-Lemaître-Robertson-Walker (FLRW) spaces using newfound embedding formulas, obtaining new and simplified expressions for the photon propagator in four dimensions. |
| title | FLRW embeddings in $\mathbb{R}^{n+2}$, differential geometry and conformal photon propagator |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2512.10901 |