No local Maxwell duality invariance

TL;DR

This paper demonstrates that in Maxwell theory, duality invariance can only have a constant parameter and cannot be localized, even when extended to curved spacetime with Einstein gravity.

Contribution

It proves that local duality invariance in Maxwell theory is impossible, extending the result to curved spacetime with Einstein gravity.

Findings

Duality rotation invariance must have a constant parameter.

Local duality invariance cannot be achieved by adding a compensating field.

Results hold in both flat and curved spacetime Maxwell theories.

Abstract

I show, in canonical formulation of flat space Maxwell theory, that its duality rotation invariance must have constant parameter, cannot be promoted to a local one by adding a compensating field, and that these conclusions hold in the curved space Maxwell-Einstein extension.