Symmetry Promotion in Electromagnetism

Abstract

A symmetric distribution of charges or currents typically produces an electromagnetic field having the same symmetry group. However, under special circumstances we show that a discrete symmetry of the source distribution leads to a larger continuous symmetry for the resulting field in restricted regions. The conditions for this promotion from discrete to continuous symmetry are that the fields be affine linear and the symmetry of the source distribution act irreducibly on the ambient space. We illustrate this effect with many examples. This phenomenon is pedagogically interesting both as a source of inspiration in electro- and magnetostatics and as an accessible example of group representation theory.