Self-Dual Maxwell Fields from Clifford Analysis
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910783053496320 |
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| author | Robson, Calum |
| author_facet | Robson, Calum |
| contents | The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra $Cl(3,1)$ these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-Dual Maxwell Fields from Clifford Analysis Robson, Calum Mathematical Physics The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra $Cl(3,1)$ these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime. |
| title | Self-Dual Maxwell Fields from Clifford Analysis |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2308.01736 |