  Based on the method of hydrodynamic projections we derive a concise formula
for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our
formula contains only quantities which are obtainable from the thermodynamic
Bethe ansatz. The Drude weight is an infinite-dimensional matrix, or bilinear
functional: it is bilinear in the currents, and each current may refer to a
general linear combination of the conserved charges of the model. As a
by-product we obtain the dynamical two-point correlation functions involving
charge and current densities at small wavelengths and long times, and in
addition the scaled covariance matrix of charge transfer. We expect that our
formulas extend to other integrable quantum models.
