On the dimensional dependence of the electromagnetic duality groups

Abstract

We study the two-fold dimensional dependence of the electromagnetic duality groups. We introduce the dual projection operation that systematically discloses the presence of an internal space of potentials where the group operation is defined. A two-fold property of the kernel in the projection is shown to define the dimensional dependence of the duality groups. The dual projection is then generalized to reveal another hidden two-dimensional structure. The new unifying concept of the external duality space remove the dimensional dependence of the kernel, allowing the presence of both $Z_2$ and SO(2) duality groups in all even dimensions. This result, ultimately unifies the notion of selfduality to all D=2k+2 dimensions. Finally, we show the presence of an unexpected duality between the internal and external spaces leading to a duality of the duality groups.