Exact many body fermi-bose transmutation in 2+1 dimensions

Abstract

We show that the low energy limit of relativistic fermions interacting with a statistical gauge field also includes a scalar interaction. When the Chern-Simons (CS) parameter μ = e²/2π and the scalar interaction is precisely that which is obtained through relativistic reduction, the many-body Hamiltonian can be solved exactly, directly in the fermion gauge, for the ground state energy which is zero and the ground state wavefunction which is gauge equivalent to one, characteristic of free bosons. Conversely, for N bosons interacting with a CS gauge field with μ=e²/2π, the mean-field ground state energy is πN²/m, which is characteristic of N free fermions.