  It is shown that planar topological effective gauge theory with dynamics,
acquires corrections to angular momentum beyond the well-known topological
photon spin, the latter arising from interactions with parity-breaking massive
fermions. In the non-relativistic limit, a first quantized Schroedinger
representation is possible where the topological and kinetic terms decouple,
the latter contributing to angular momentum and compete with the centrifugal
barrier. This results in shallow resonances of Efimov kind, which may be
verified in planar physical systems.
