  Using algebraic Bethe ansatz and the solution of the quantum inverse
scattering problem, we compute compact representations of the spin-spin
correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At
lattice distance m, they are typically given as the sum of m terms. Each term n
of this sum, n = 1,...,m is represented in the thermodynamic limit as a
multiple integral of order 2n+1; the integrand depends on the distance as the
power m of some simple function. The root of these results is the derivation of
a compact formula for the multiple action on a general quantum state of the
chain of transfer matrix operators for arbitrary values of their spectral
parameters.
