A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism

We study boson-fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well as the configuration-space approach to indistinguishable particles, we find a generalization of the boson-fermion duality between the Lieb-Liniger model and the Cheon-Shigehara model. We present an explicit construction of $n$-boson and $n$-fermion models which are dual to each other and characterized by $n-1$ distinct (coordinate-dependent) coupling constants. These models enjoy the spectral equivalence, the boson-fermion mapping, and the strong-weak duality. We also discuss a scale-invariant generalization of the boson-fermion duality.