Generalised Maxwell Equations in Higher Dimensions

作者：Eelbode David; Roels Matthias^*

来源：Complex Analysis and Operator Theory, 2016, 10(2): 267-293.

DOI：10.1007/s11785-014-0436-5

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.

• 出版日期2016-2