On the non-relativistic limit of the quantum sine-Gordon model with integrable boundary condition

TL;DR

This paper demonstrates that the non-relativistic limit of the quantum sine-Gordon model with boundary conditions can be described by a generalized Calogero-Moser model with a P"oschl-Teller boundary potential.

Contribution

It establishes a connection between the quantum sine-Gordon model with boundary conditions and the Calogero-Moser model in the non-relativistic limit, providing a new integrable systems correspondence.

Findings

The non-relativistic limit of the quantum sine-Gordon model corresponds to a Calogero-Moser model.

The boundary conditions translate into a P"oschl-Teller boundary potential.

The models are shown to be equivalent in the non-relativistic regime.

Abstract

We show that the the generalized Calogero-Moser model with boundary potential of the P\"oschl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with Dirichlet boundary condition.