1cexpansion of the density matrix for theδ-function Bose gas

We study the strong-coupling ($c\to \infty$) expansion of the correlation functions for the one-dimensional $\delta$-function Bose gas at zero temperature. Making use of the Bethe's-hypothesis wave functions, we calculate exactly the two-point function (up to the order $\frac{1}{c^2}$) and the $n$-point functions (up to the order $\frac{1}{c}$), both in the finite box and in the thermodynamic limit. This generalizes the recent result of Creamer, Thacker, and Wilkinson for the $\frac{1}{c}$ correction to the two-point function.