On local duality invariance in electromagnetism

Abstract

Duality is one of the oldest known symmetries of Maxwell equations. In recent years the significance of duality symmetry has been recognized in superstrings and high energy physics and there has been a renewed interest on the question of local duality rotation invariance. In the present paper we re-visit global duality symmetry in the Maxwell action and delineate the ambiguous role of gauge invariance and time locality. We have recently demonstrated that local duality invariance in a Lorentz covariant form can be carried out in the Maxwell equations. In this paper it is shown that in the four-pseudo vector Lagrangian theory of Sudbery a local duality generalization can be naturally and unambiguously implemented and the Euler-Lagrange equations of motion are consistent with the generalized Maxwell field equations. It is pointed out that the extension of Noether theorem in full generality for a vector action is an important open problem in mathematical physics. Physical consequences of this theory for polarized light and topological insulators are also discussed.