  We present a continuum operator map that inverts the role of particles and
antiparticles in three dimensional QED. This is accomplished by the attachment
of specific holomorphic Wilson lines to Dirac fermions. We show that this
nonlocal map provides a continuum realization of Son's composite fermions at
$\nu = \frac{1}{2}$. The inversion of Landau levels and the
Dirac-cone--composite-Fermion duality is explicitly demonstrated for the case
of slowly varying magnetic fields. The role of Maxwell-terms as well as the
connection of this construction to a gauge-invariant formulation of 3D gauge
theories is also elaborated upon.
