Abstract
This paper deals with the generalisation of the classical Maxwell equations to arbitrary dimension $$m$$ 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.
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