Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction

Abstract

For a system of spinless one-dimensional fermions, the non-vanishing short-range limit of two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this fermionic system and the bosonic particle system with two-body $\delta$-function interaction with the reversed role of strong and weak couplings. KEYWORDS: one-dimensional system, $ϵ$-interaction, solvable many-body problem, exact bosonization

Comments: 4 pages ReVTeX 4 epsf figures included, new Refs