Galilean and Carrollian Hodge star operators
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913244893937664 |
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| author | Fecko, Marián |
| author_facet | Fecko, Marián |
| contents | The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09788 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Galilean and Carrollian Hodge star operators Fecko, Marián Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics. |
| title | Galilean and Carrollian Hodge star operators |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2206.09788 |