Free-Fermionic Description of the Repulsive Nonlinear Schrödinger Model

Abstract

It is shown that in an infinite volume, the nonlinear Schrodinger model (repulsive case) is equivalent to a nonrelativistic free-fermion field theory. This is accomplished by expressing the Hamiltonian, momentum operator and particle density operator in terms of free-fermion operators constructed out of reflection operators. It is also shown that a thermodynamic trace of the density operator can be consistently regularized so as to yield a Fermi-Dirac distribution.