Boson-Fermion transmutation in (2+1) dimensions

Renewed interest in three-dimensional field theory is spurred by the planar character of high TC superconducting antiferromagnets. We prove Polyakov's conjecture that a CP1 complex scalar field in three spacetime dimensions, coupled to an external gauge field with a particular Chern-Simons term, is equivalent, at low momenta, to one neutral fermion. We find that this fermion has a (strong) Thirring potential. This is the whole content, at long wavelengths, of the Hubbard model. If the gauged group is abelian, a few decoupled Goldstone bosons survive as well. The dressing of a scalar field to become fermionic is similar to a Higgs mechanism. (orig.)