Electromagnetism and the holomorphic properties of spacetime

The Cauchy–Riemann equations of holomorphy are extended to fields in higher-dimensional spaces in a framework of Clifford algebras. The equations of holomorphy in Minkowski spacetime turn out to be the Maxwell equations in vacuum. The Lorentz gauge condition is a result of the holomorphy. Sources can be included in an extension of the residue theorem, where charges correspond to the residues.