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

• URL: http://arxiv.org/abs/2105.04288v2
• Date: Fri, 29 Oct 2021 12:00:00 GMT
• Title: A Generalization of the One-Dimensional Boson-Fermion Duality Through the Path-Integral Formalism
• Authors: Satoshi Ohya
• Abstract summary: We study boson-fermion dualities in one-dimensional many-body problems. We find a generalization of the boson-fermion duality between the Lieb-Liniger model and the Cheon-Shigehara model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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