Generalised Maxwell equations in higher dimensions
Faculty of Sciences. Mathematics and Computer Science
Complex analysis and operator theory
, p. 267-293
University of Antwerp
This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension and their connections with the Rarita-Schwinger equation. This is done using the framework of Clifford analysis, a multivariate function theory in which arbitrary irreducible representations for the spin group can be realised in terms of polynomials satisfying a system of differential equations. This allows the construction of generalised wave equations in terms of the unique conformally invariant second-order operator acting on harmonic-valued functions. We prove the ellipticity of this operator and use this to investigate the kernel, focusing on both polynomial solutions and the fundamental solution.