Antiparticles as Particles: QED_{2+1} and Composite Fermions at ν=1/2.
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 ν=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.