  The idea of gauging (i.e. making local) symmetries of a physical system is a
central feature of many modern field theories. Usually, one starts with a
Lagrangian for some scalar or spinor matter fields, with the Lagrangian being
invariant under a global phase symmetry transformation of the matter fields.
Making this global phase symmetry local results in the introduction of vector
fields. The vector fields can be said to arise as a result of the gauge
principle. Here we show that this chain of reasoning can be reversed: by
gauging the electric-magnetic dual symmetry of a Lagrangian which originally
contains only the vector gauge fields we find that it is necessary to introduce
matter fields (scalar fields in our example). In this gauging of the
electric-magnetic dual symmetry the traditional roles of the vector fields and
the matter fields are interchanged.
