Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions

For a system of spinless one-dimensional fermions, the nonvanishing short-range limit of a 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 a two-body $\delta$-function interaction with the reversed role of strong and weak couplings.