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

TL;DR

This paper generalizes the one-dimensional boson-fermion duality by constructing dual models with coordinate-dependent couplings, revealing spectral equivalence and strong-weak duality using path-integral and configuration-space formalisms.

Contribution

It introduces a broad class of dual boson-fermion models with variable couplings, extending the known Lieb-Liniger and Cheon-Shigehara duality framework.

Findings

Constructed explicit dual models with coordinate-dependent couplings.

Demonstrated spectral equivalence and boson-fermion mapping.

Established a scale-invariant generalization of the duality.

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.