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

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.