The Hubbard chain: Lieb-Wu equations and norm of the eigenfunctions

We argue that the square of the norm of the Hubbard wave function is proportional to the determinant of a matrix, which is obtained by linearization of the Lieb-Wu equations around a solution. This means that in the vicinity of a solution the Lieb-Wu equations are non-degenerate, if the corresponding wave function is non-zero. We further derive an action that generates the Lieb-Wu equations and express our determinant formula for the square of the norm in terms of the Hessian determinant of this action.