A generalization of the one-dimensional boson–fermion duality through the path-integral formalism

Abstract

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.