Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914121978478592 |
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| author | Garzón, Manuel López-Martínez, Salvador |
| author_facet | Garzón, Manuel López-Martínez, Salvador |
| contents | We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is present, although the vector potential assumes a leading role. The approach is based on minimizing the action functional associated with the relativistic Lagrangian. The compactness of the minimizing sequences requires the existence of negative values for the functional, which is proven using novel ideas that exploit the sign-indefinite nature of the term involving the vector potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential Garzón, Manuel López-Martínez, Salvador Dynamical Systems Mathematical Physics Analysis of PDEs 34C25, 37J51, 78M30 We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is present, although the vector potential assumes a leading role. The approach is based on minimizing the action functional associated with the relativistic Lagrangian. The compactness of the minimizing sequences requires the existence of negative values for the functional, which is proven using novel ideas that exploit the sign-indefinite nature of the term involving the vector potential. |
| title | Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential |
| topic | Dynamical Systems Mathematical Physics Analysis of PDEs 34C25, 37J51, 78M30 |
| url | https://arxiv.org/abs/2510.25462 |