  Bunster and Henneaux and, separately, Deser have very recently considered the
possibility of gauging the usual electromagnetic duality of Maxwell equations.
By using off-shell manipulations in the context of the Principle of least
action, they conclude that this is not possible, at least with the conventional
compensating gauge fields scheme. Such a conclusion contradicts, however, an
old result of Malik and Pradhan, who showed that it is indeed possible to
introduce an extra abelian gauge field directly in the vacuum Maxwell equations
in order to render them covariant under local duality transformations. Since it
is well known that the equations of motion can, in general, admit more
symmetries than the associate Lagrangian, this would not be a paradoxal result,
in principle. Here, we revisit these works and identify the source of the
different conclusions. We show that the Malik-Pradhan procedure does not
preserve the original Maxwell gauge invariance, while Bunster, Henneaux, and
Deser sought for generalizations which are, by construction, invariant under
the Maxwell gauge transformation. Further, we show that the Malik-Pradhan
construction cannot be adapted or extended in order to preserve the Maxwell
gauge invariance, reinforcing the conclusion that it is not possible to gauge
the electromagnetic duality.
