Electromagnetism: an intrinsic approach to Hadamard's method of descent
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913878526394368 |
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| author | Angelone, Giuliano Ercolessi, Elisa Facchi, Paolo Maggi, Rocco Marmo, Giuseppe Pascazio, Saverio Pepe, Francesco V. |
| author_facet | Angelone, Giuliano Ercolessi, Elisa Facchi, Paolo Maggi, Rocco Marmo, Giuseppe Pascazio, Saverio Pepe, Francesco V. |
| contents | We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge star operator, we implement descent conditions on differential forms that reduce Maxwell's equations in four-dimensional spacetime to electromagnetic theories in lower dimensions. We also consider multiple descent along pairwise commuting vector fields of invariance, yielding a finer decomposition of Maxwell's equations. Our results provide a unified and geometrically transparent interpretation of dimensional reduction, with potential applications to field theories in lower-dimensional spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electromagnetism: an intrinsic approach to Hadamard's method of descent Angelone, Giuliano Ercolessi, Elisa Facchi, Paolo Maggi, Rocco Marmo, Giuseppe Pascazio, Saverio Pepe, Francesco V. Mathematical Physics Classical Physics We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge star operator, we implement descent conditions on differential forms that reduce Maxwell's equations in four-dimensional spacetime to electromagnetic theories in lower dimensions. We also consider multiple descent along pairwise commuting vector fields of invariance, yielding a finer decomposition of Maxwell's equations. Our results provide a unified and geometrically transparent interpretation of dimensional reduction, with potential applications to field theories in lower-dimensional spacetimes. |
| title | Electromagnetism: an intrinsic approach to Hadamard's method of descent |
| topic | Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2506.05255 |