A biquaternionic reformulation of Maxwell's equations via Fourier analysis
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911709006921728 |
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| author | Guillén-Villalobos, Aarón Delgado, Briceyda B. Rodríguez, Héctor Vargas |
| author_facet | Guillén-Villalobos, Aarón Delgado, Briceyda B. Rodríguez, Héctor Vargas |
| contents | We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery provided by the Fourier transform, we fully characterize the Fourier transform of a fundamental solution of this operator and construct a well-defined right inverse operator. As an application, we derive explicit vectorial solutions to the time-dependent Maxwell system, extending prior biquaternionic approaches. These tools offer analytical efficiency for complex electromagnetic problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A biquaternionic reformulation of Maxwell's equations via Fourier analysis Guillén-Villalobos, Aarón Delgado, Briceyda B. Rodríguez, Héctor Vargas Analysis of PDEs 42A38, 47S02, 35Q61, 30G35 We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery provided by the Fourier transform, we fully characterize the Fourier transform of a fundamental solution of this operator and construct a well-defined right inverse operator. As an application, we derive explicit vectorial solutions to the time-dependent Maxwell system, extending prior biquaternionic approaches. These tools offer analytical efficiency for complex electromagnetic problems. |
| title | A biquaternionic reformulation of Maxwell's equations via Fourier analysis |
| topic | Analysis of PDEs 42A38, 47S02, 35Q61, 30G35 |
| url | https://arxiv.org/abs/2605.21412 |