Duality transformations of Abelian and non-Abelian gauge fields

Abstract

Duality transformations, i.e., rotations of electric and magnetic fields into each other, are implementable by a time-local generator for source-free Maxwell theory in an arbitrary spacetime metric. The Maxwell action ∫(E^2 − B^2) as well as the stress tensor components, e.g., E^2 + B^2, are duality invariant and the generator is conserved. In the formally analogous Yang-Mills case, duality transformations cannot even be consistently implemented.