Self-Dual Maxwell Fields from Clifford Analysis
arXiv:2308.01736 · doi:10.1007/s00006-024-01368-1
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 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.
13 pages, as published