Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra ${\cal U}_q (\hat{sl}_2)$ together with the corner transfer matrix approach (massive regime).