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For a system of spinless one-dimensional fermions, the non-vanishingshort-range limit of two-body interaction is shown to induce the wave-functiondiscontinuity. We prove the equivalence of this fermionic system and thebosonic particle system with two-body $\delta$-function interaction with thereversed role of strong and weak couplings.  KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-bodyproblem, exact bosonizationComment: 4 pages ReVTeX 4 epsf figures included, new Ref

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