Self-dual Maxwell fields from Clifford analysis

Robson, Calum (2025) Self-dual Maxwell fields from Clifford analysis. Advances in Applied Clifford Algebras, 35 (1). ISSN 0188-7009

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Abstract

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.

Item Type:	Article
Additional Information:	© 2024 The Author
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	03 Dec 2024 12:18
Last Modified:	20 Dec 2024 14:33
URI:	http://eprints.lse.ac.uk/id/eprint/126220

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