The propagator of the attractive delta-Bose gas in one dimension

TL;DR

This paper extends the exact quantum propagator for the delta-Bose gas from repulsive to attractive interactions and confirms the completeness of Bethe ansatz eigenfunctions through analytic continuation.

Contribution

It provides the first explicit analytic continuation of the propagator to attractive interactions and independently proves the completeness of Bethe ansatz eigenfunctions.

Findings

Successfully continued the propagator to attractive interactions.

Confirmed the completeness of Bethe ansatz eigenfunctions.

Established connections between the propagator expansion and Bethe ansatz.

Abstract

We consider the quantum delta-Bose gas on the infinite line. For repulsive interactions, Tracy and Widom have obtained an exact formula for the quantum propagator. In our contribution we explicitly perform its analytic continuation to attractive interactions. We also study the connection to the expansion of the propagator in terms of the Bethe ansatz eigenfunctions. Thereby we provide an independent proof of their completeness.